oJi-nson 


SCHOOL  ARITHMETIC 

"Pri 


rimar 


IRLF 


E7fi 


Mi 


\J&- 


<M 


•Joh 
Richmond  -^Virginia 


IN  MEMORIAM 
FLOR1AN  CAJORI 


SCHOOL    ARITHMETIC 


PRIMARY   BOOK 


BY 

JOHN  M.  COLAW,  A.  M. 

ASSOCIATE   EDITOR  OF  THE   AMERICAN   MATHEMATICAL   MONTHLY, 
MONTEREY,  VA. 


J.  K.  ELLWOOD,  A.  M. 


PRINCIPAL  OF  THE  COLFAX  PUBLIC  SCHOOL,    PITTSBURG,  PA.,  AUTHOR  OF 
TABLE  BOOK   AND  TEST  PROBLEMS   IN   ELEMENTARY   MATHEMATICS. 


RICHMOND,  VA. 
B.  F.  JOHNSON  PUBLISHING  CO. 

1900 


JOHNSON  SERIES 

SCHOOL  ARITHMETICS 


..BY.. 
COLAW  AND  ELLWOOD 


Primary 


Wnrfc 


2£i  Pages          Price,  35  Cents  • 
^ 

Advanced  Book 


With  an  Introduction  to  Algebra 
442  Pages  Price,  60  Cents 

<£ 
HANDBOOK  FOR  TEACHERS 

Containing  Suggestions  as  to  the  best  methods  of 
teachiTfc  Arithmetic^  an*  scl.urti6ns  of  diffi- 
"  ' 


fook 
«  t.     »   (Jll  Prcjwation)  ^ 


CAJORI 


Copyright,  1900.  by 
J.  M.  COLAW  and  J.  K.  ELLWOOD. 


PREFACE. 


TTTO  DEVELOP  in  the  pupil's  mind  the  idea  of  number  and 
its  uses,  to  give*  him  facility  in  numerical  operations,  and 
«-k  to  lead  him  to  grasp  firmly  the  principles  involved  requires 
the  serious  effort  of  the  most  skilful  teacher.  The  most  any 
author  can  do  to  aid  him  is  to  present,  in  more  or  less  detail, 
an  outline  of  a  practical  scheme  of  instruction  based  upon  the 
latest  and  best  thought  in  number  teaching;  and  even  this  is 
a  task  that  none  but  the  superficial  would  undertake  without 
"  fear  and  trembling."  Neither  theory  nor  practice  alone  is 
a  sufficient  endowment  for  the  work.  Every  theory,  every 
method,  every  device  must  be  weighed  in  the  class-room  balance. 
That  which  is  to  be  taught  is  the  child — not  arithmetic. 

Holding  these  views,  the  writers  of  this  book  have  spared 
no  effort  in  its  preparation.  With  a  wholesome  respect  for  the 
injunction,  "  Prove  all  things;  hold  fast  that  which  is  good," 
they  have  endeavored  to  steer  carefully  between  the  Scylla  of 
modern  fad  and  the  Charybdis  of  mechanical  drudgery  and 
stupefying  monotony.  Their  aim  has  been  to  furnish  for  the 
teacher  a  sound  and  practical  work  presenting  the  matter  in 
an  approved  order  and  suggesting  rational  methods  of  obtaining 
the  most  desirable  results.  As  to  how  well  they  have  succeeded 
the  teacher  must  decide. 

ARRANGEMENT. — Before  entering  school  the  child  learns  a 
little  of  a  great  many  things,  not  a  great  deal  about  one  thing. 
There  is  no  topical  arrangement  in  nature.  "And  Nature,  the 
dear  old  nurse,"  permits  the  order  of  the  child's  mental  develop- 
ment to  determine  the  arrangement  of  the  material,  which  is 
always  a  progressive  one.  The  child  learns  a  little  about  many 
things  to-day,  a  little  more  to-morrow,  adds  an  increment  to 
his  knowledge  and  widens  his  range  of  subjects  day  by  day. 
This  arrangement  keeps  interest  alive,  without  which  there  is 
no  substantial  progress.  This  book  aims  to  follow  the  natural 

[v] 


911274 


VI  PREFACE. 

order  as   closely  as   may  be,   considering  the  conditions   under 
which  teachers  are  required  to  work. 

"  FBOM  THE  CONCRETE  TO  THE  ABSTRACT." — The  child's  mind 
must  be  approached  through  those  ever  open  doors,  the  senses. 
Primary  number  teaching  must  be  begun  by  the  pupil's  observ- 
ing and  handling  objects,  yet  the  mere  presence  of  concrete 
things  does  not  guarantee  the  presence  of  definite  numerical 
ideas  in  the  mind  of  the  pupil.  They  must  be  so  presented  as 
to  stimulate  and  aid  the  mental  movement  of  discriminating 
and  relating  which  leads  to  definite  ideas  of  number.  The 
mind  must  (r/)  recognize  the  like  objects  as  distinct  individuals, 
and  (/>)  group  (put  together)  the  objects  into  a  whole.  The 
child's  own  activity  must  conceive  a  whole  of  parts,  and  relate 
the  parts  in  a  definite  whole.  It  is  not  enough  that  he  knows 
our  country  as  45  states;  he  must  know  the  45  states  as  one 
country.  He  should  recognize  five,  for  example,  not  only  as 
five  ones,  but  also  as  one  flue,  considering  the  component  ones 
not  chiefly  for  their  own  sake,  but  as  giving  definite  value  to 
the  whole,  the  group.  By  repeated  acts  of  such  measurement 
or  valuation  the  mind  advances  naturally  and  inevitably  from 
things  to  relations,  from  facts  to  principles,  from  the  concrete 
to  the  abstract.  Believing  that  the  concept  of  ratio — an  abstract 
idea — must  be  evolved  in  the  young  mind  by  its  own  activity, 
and  that  therefore  it  should  not  be  thrown  at  the  child  in  the 
earlier  stages  of  his  progress,  the  authors  have  not  explicitly 
stated  the  ratio  idea  until  it  has  had  time  to  grow  into  a 
recognizable  and  useful  product  of  the  pupil's  mind. 

MATERIAL. — The  objects  called  for  in  this  book,  such  as  cubes, 
splints,  foot  rules,  quart  measures,  etc.,  can  be  provided  by 
the  teacher  with  little  trouble,  and  their  use  should  precede 
that  of  pictures  and  words.  How  long  their  use  should  be 
continued  with  any  given  class  must  be  determined  by  the 
teacher.  They  should  certainly  not  be  laid  aside  until  the  child 
can  bring  their  images  into  consciousness  without  the  presen- 
tation of  the  actual  objects  to  his  senses;  but  when  these  images 
are  within  easy  reach,  their  use  should  supersede  that  of  objects. 
The  number  pictures  given  in  this  book  are  an  important  aid 
to  the  child's  mental  movement  of  abstracting  and  relating, 
and  must  be  used  for  economy  of  energy.  Five  dots  analytically 
arranged  *•*  are  more  easily  grasped  than  five  dots  placed 


PREFACE.  vil 

promiscuously,  or  even  in  a  row.  Moreover,  they  are  perceived 
as  one  whole,  rather  than  as  separate,  unrelated  parts,  and 
they  should  symbolize  any  five  units  whatever — five  $2  or  five 
10-ft.  as  well  as  five  $1  or  five  1-ft.  In  the  perceptive  form 

•  •  •  •  ,  twelve  is  seen  as  three  fours  and  as  four  threes — as  four 

•  •  •  9 

three  times  and  as  three  four  times — and  the  child's  idea  of  the 
number  is  more  definite  than  when  the  whole  was  measured 
by  but  one  unit,  the  individual.  Besides,  this  use  of  pictures 
suggests  to  the  pupil  a  method  by  which  he  can  discover  for 
himself  the  measuring  units  of  quantity  or  determine  the  definite 
value  of  a  whole.  In  notation,  fractions,  measurement  of 
surfaces,  etc.,  the  illustrations  will  be  found  highly  beneficial; 
their  purpose  is  to  aid,  not  to  ornament. 

COUNTING — MEASURING. — Dr.  Harris  says,  "  The  first  lessons 
in  arithmetic  should  be  based  on  the  practice  of  measuring  in 
its  varied  applications."  In  its  earlier  stages  measurement  is 
a  vague  estimate,  a  crude  guess.  Later  an  undefined  unit  of 
measure  is  used  to  make  a  whole  more  definite,  as  when  a 
class  is  measured  by  the  unit  boy — an  unmeasured  unit.  But 
it  is  only  when  the  unit  itself  is  accurately  defined  that  precise 
numerical  value  is  reached.  The  immediate  purpose  of  measur- 
ing is  to  make  some  whole  more  definite — to  find  hoir  much 
there  is  of  it.  This  can  be  done  by  learning  how  many  units 
are  in  it,  and  the  "  how  many  "  can  be  found  only  by  counting; 
hence  measuring  involves  rational  counting — the  finding  of  the 
SUM  of  the  units  that  compose  a  whole.  It  seems  clear,  there- 
fore, that  the  child  learning  to  count  should  be  led  to  number 
the  parts  that  make  up  some  whole,  as  the  desks  in  a  row — to 
count  with  a  definite  cud  in  view;  that  the  starting  point  should 
be  a  group  of  things — a  whole  to  measure,  parts  to  count  and 
relate.  As  soon  as  possible  there  should  also  be  exact  measure- 
ments. The  foot  may  be  taken  as  the  whole  and  measured  by 
4-inch  units,  3-inch  units,  etc.  Not  only  the  idea  of  number 
as  the  repetition  of  a  unit  of  measure  to  equal  a  magnitude, 
but  also  the  law  of  commutation  will  be  slowly,  perhaps,  but 
surely  developed  through  the  use  of  the  facts  supplied  by  sense- 
perception  in  the  rational  use  of  objects  and  number  pictures. 

FIGURE  PROCESSES  OXI.Y  THE  MEANS  TO  AN  END. — The  child 
must  learn  figure  processes,  not  for  their  own  sake,  but  as  an  aid 
in  discerning  relation.  Figures  are  not  at  all  necessary  to 


Vlll  PREFACE. 

numerical  perception,  but  when  this  is  to  be  supplanted  by 
numerical  facility  they  should  be  employed  as  a  cpnvenient 
tool.  The  real  subjects  of  thought  are  magnitudes  (of  value,  of 
space,  of  weight,  etc.)  and  their  relations;  figures  are  mere 
symbols  of  these.  The  essential  thing  is  the  discernment  of 
relation  by  comparing  magnitudes;  figure  processes  may  or 
may  not  be  an  aid  in  securing  this  end — they  can  never  be 
anything  more.  It  is  evident,  therefore,  that  the  mere  manipu- 
lation of  figures — the  mechanical  work — is  of  small  value  in 
comparison  with  the  thought  processes — the  mental  work; 
yet  as  the  means  to  an  end  it  is  of  great  importance,  and  to 
secure  absolute  accuracy  therein  should  be  the  constant  aim 
of  every  teacher. 

SUGGESTIVE  QUESTIONS  AND  DIRECTIONS. — The  exercises  of 
this  book  are  more  abundant  and  varied  than  is  usual  in  books 
of  this  kind,  and  much  additional  work  will  be  called  forth 
by  the  suggestive  nature  of  many  of  the  questions  and  directions. 
There  is  an  especial  need  of  an  abundance  of  constructive 
exercises.  The  pupil  must  be  active,  must  do  as  well  as  see. 
Knoiciny  and  doing  are  correlative.  Things  are  grasped  most 
readily  when  there  is  a  necessity,  real  or  apparent,  for  knowing 
them.  Boys  who  sell  papers  or  fruit  on  the  streets,  being  under 
the  necessity  of  computing  and  making  change,  enter  school 
with  a  surprising  stock  of  number  facts.  Excellent  number 
woik  may  be  had  in  connection  with  the  occupations  of  the 
school-room — passing  pencils,  making  boxes,  modeling,  playing 
number  games,  measuring  things  used  in  nature  study  and 
manual  training,  etc.  The  questions  and  directions  given 
indicate  the  kind  of>work  that  should  be  done,  but  the  quantity 
of  it  needed  must  be  determined  by  the  teacher,  and  by  him 
supplied  when  necessary.  Figures  and  signs  are  not  used  until 
the  child  has  acquired  some  familiarity  with  the  names  of 
numbers  to  twelve  and  with  a  few  of  the  simpler  processes  and 
facts.  This  should  at  least  suggest  that  the  figure  symbol 
should  not  be  given  until  the  child  can  understand  that  it  is  a 
mere  mechanical  tool  by  which  he  can  obtain  rapid  and  at  the 
same  time  equally  true  results. 

It  is  neither  necessary  nor  desirable  to  keep  this  book  out 
of  the  hands  of  young  pupils  until  they  are  able  to  read  it 
with  ease.  They  should  at  least  get  the  benefit  of  the  number 
pictures  and  the  picture  exercises.  Anything  too  difficult  for  the 


PREFACE.  IX 

children  should  be  read  by  the  teacher,  and  answers  only  required 
of  the  pupils.  Formal  analysis  should  be  deferred;  when 
insisted  upon  at  too  early  a  stage,  it  interferes  with  progress 
and  deadens  the  pupil's  interest. 

It  is  believed  that  in  plan,  matter,  and  method  this  book  is  in 
substantial  accord  with  the  views  of  progressive  teachers  in 
the  best  schools,  and  that  it  will  prove  a  suitable  foundation 
for  and  introduction  to  the  more  formal  and  rigorous  treatment 
presented  in  the  Advanced  book  of  the  series.  Its  contents  are 
such,  however,  that  pupils  who  can,  complete  only  this  book 
will  find  themselves  fitted  to  cope  with  the  ordinary  problems 
of  every-day  life. 

THE  AUTHORS. 

July  2,  WOO. 


CONTENTS. 


FIRST  STEPS: 

Indefinite  Comparison,  Form,  Counting,  Measuring — 

Use  of  Ruler,  Concrete  Exercises        ....  1-43 

PRIMARY  NUMBER  WORK  : 

Numbers  to  10— Combinations  (Emphasis  on  Adding 
and  Subtracting),  Pint,  Quart,  Gallon,  Half,  Fourth, 

Third,  Peck,  Bushel 44-74 

Tens .        .  74-83 

Review  and  Drill 84-91 

Writing  and  Reading  Numbers  from  1  to  100        .        .  92-95 

The  Signs  X  and  -h- 96-99 

Numbers  to  20 —Tens  and  Ones,  Combinations,  Month, 

Year,  Roman  Notation,  Fifth,  Ounce,  Pound,  Sixth,  100-134 

Review  and  Drill 135-136 

Twenty— Two  Tens,  Tenth 137-142 

Numbers  to  100— Development  of  Tens  and  Ones          .  143-147 

Addition  and  Subtraction    .     .        .        .        .         .  148-154 

Numbers  to  30— Table  of  3's,  'Square  Foot,  Easy  Areas,  155-160 

Numbers  to  40— Table  of  4's           .'....  161-168 

Numbers  to  50— Table  of  5's,  Square  Yard    .        .        .  169-173 

Addition  and  Subtraction 174-188 

Numbers  to  60— Table  of  6's,  Hour,  Minute,  Second    .  189-195 

Numbers  to  70— Table  of  7' s 196-202 

Numbers  to  80— Table  of  8's,  Perimeter        .         .        .  203-208 

Numbers  to  100-Table  of  9's,  Cubic  Inch     .        .        .  209-216 

Review  and  Drill  Work 217-227 

Hundreds— Cent,  Dollar 228-232 

Hundreds  and  Tens -.        .  233-235 

(xi) 


Xll 


CONTENTS. 


ARTICLE. 

Hundreds,  Tens,  and  Ones     .        .        .        .        .        .  236-238 

Addition  and  Subtraction        .        .         .        .        .  239-242 

Multiplication  and  Division 243-250 

U.  S.  Money— Making  Change 251-260 

Numbers  to  Millions— Unit  of  Measure,  Notation  and 

Numeration 261-271 

Addition  and  Subtraction 272-276 

Multiplication  and  Division 277-295 

Review  Work           .  •       . 296-297 

U.  S.  Money  and  Decimals 298-306 

COMMON  FRACTIONS  : 

Halves,  Fourths,  Eighths,  Thirds,  Sixths,  Twelfths- 
Fifths,  Tenths,  Hundredths  —  Relations,  Common 
Denominator,  Addition  and  Subtraction,  Mtiltiplica- 

and  Division 307-333 

COMPOUND  NUMBERS 334-355 

DECIMAL  FRACTIONS 356-370 

PERCENTAGE     . 371-374 

INTEREST 375-376 

GENERAL  REVIEW    .  3/7-378 


SCHOOL   ARITHMETIC. 


FIRST    STEPS. 


Comparison. 
-A 


0 B 

O-  C 

1.   The  line  OB  is  longer  than  which  line? 

The  line  OB  is  shorter  than  which  line? 

The  line  OA  is  shorter  than  which  lines? 

The  line  OC  is  longer  than  which  lines? 

Which  line  is  longer  than  the  line  OB? 

Which  lines  are  shorter  than  the  line  OC? 

"Which  line  is  shorter  than  the  line  OB? 

Is  any  one  of  these  lines  longer  than  the  line  OC? 

Is  any  one  shorter  than  the  line  OA? 


A 

B 
C 

\l 

0 

P 

2.  Cut  splints  the  same  length  as  A,  B?  and  C. 

Show  me  the  longest. 
Show  me  the  next  longest. 


SCHOOL    ARITHMETIC. 


Show  me  the  shortest. 

Show  me  the  next  shortest. 

How  many  of  these  splints  are    longer  than  B? 

How  many  of  these  splints  are  longer  than  A? 

How  many  of  these  splints  are  shorter  than  B? 

How  many  of  these  splints  are  shorter  than  C? 


A  B 

3.  Blocks  of  this  shape  are  called  cubes. 
Which  is  the  largest  cube? 
Which  is  the  next  largest  cube? 
Which  is  the  smallest  cube? 
Which  is  the  next  smallest  cube? 
HOAV  many  cubes  are  larger  than  C? 
How  many  cubes  are  smaller  than  A? 
What  can  you  tell  me  about  B? 

4    Which  is  longer,  the  length  of  your  desk  or  its  width  ? 

Which  is  wider,  the  sidewalk  or  the  street? 

Which  is  longer,  your  arithmetic  or  your  slate? 

Which  is  thicker,  your  book  or  your  slate? 

Which  is  larger,  a  boy  or  a  man? 

Which  is  higher,  your  house  or  the  school-house? 


COMPARISON. 


5.  Here  are  two  groups  of  cubes.  fj| 
"Which  is  the  larger  group?  f|] 

How  many  more  cubes  in  the  larger  group  than  in  the 
smaller  one? 


AVliich  of  these  rings  has  the  most  dots  in  it? 

The  ring  on  the  left  has  how  many  more  dots  than  the 
one  on  the  right? 

Are  there  more  girls  than  boys  in  the  class?  How  many 
more? 

NOTE. — Children  should  be  given  sufficient  exercise  in  making 
comparison  to  familiarize  them  with  the  use  of  the  terms  longer, 
shorter,  larger,  smaller,  JiiyJier,  irider,  etc.  They  may  compare 
solids,  surfaces,  lines,  sounds,  or  any  objects  within  reach  or  sight. 


6.  Here  are  pictures  of  a  square,  a  circle,  a  triangle, 
and  a  sphere. 

Show  me  the  square.     Show  me  the  circle. 

Xow  show  me  the  triangle.     Show  me  the  sphere. 

Take  four  sticks  of  the  same  length  and  make  a  square. 

Cut  a  square  out  of  paper.  Xame  something  that 
resembles  a  square  in  shape. 


4:  SCHOOL    ARITHMETIC. 

From  pasteboard  cut  out  six  equal  squares.  Make  a 
box  of  them.  What  have  you?  Name  some  object  shaped, 
like  a  cube. 

Lay  a  penny  on  paper  and  draw  a  line  around  it. 

Cut  out  the  circle.  Name  something  that  is  a  circle 
in  shape. 

Draw  a  square  on  the  blackboard.     Now  draw  a  circle. 

Did  you  draw  straight  lines  in  making  the  square? 
What  kind  of  line  around  the  circle? 

Here  is  a  marble.  What  is  it  shaped  like  ?  Is  your  ball 
a  sphere?  What  part  of  the  body  is  almost  a  sphere? 

NOTE. — Have  pupils  observe  and  handle  solids  until  they  know 
the  familiar  cube,  sphere,  square,  triangle,  circle.  Have  them 
model  simple  forms,  and  cut  squares,  circles,  etc.,  from  paper. 

Counting  to  Twelve. 

7.   How  many  boys  are  in  the  class?     How  many  girls? 

How  many  seats  are  in  this  row? 

How  many  sides  has  this  square? 

Count  the  faces  of  this  cube. 

How  many  pairs  of  shoes  in  the  class? 

How  many  groups  of  three  blocks? 

m         m 
mmm        mm        mm 

Here  are  twelve  spools.  Arrange  them  in  pairs,  and 
count  the  number  of  pairs. 

Arrange  them  in  groups  of  three,  and  count  the  groups. 


MEASURING USE    OF    RULER. 


Here  are  some  dots. 
How  many  twos? 
How  many  threes? 
How  many  fours? 


Measuring — Use  of  Ruler. 

8.  This  line  -  -  is  an  inch  long. 

Draw  a  line  as  long  as  the  one  above. 
Cut  four  sticks  each  as  long  as  the  line.     How  long  is 
each  stick? 

How  many  sticks  are  as  long  as  the  line  below? 


Then  how  long  is  this  line? 

Find  how  many  inches  wide  this  book  is. 

How  long  is  your  pencil? 

Draw  a  line  four  inches  long. 

An  inch  lower,  draw  another  line  four  inches  long. 

Rule  a  page  of  this  paper  with  lines  an  inch  apart. 

9.  How  long  is  this  square?    How  wide 
is  it? 

Are  all  four  sides  of  the  same  length? 

A  square   that  is  an  inch  on  a  side  is 
called  a  square  inch. 

Draw  a  square  inch  on  paper.     Cut  it 
out. 


6 


SCHOOL    ARITHMETIC. 


Cut  out  a  piece  of  paper  two  inches  long  and  one  inch 
wide. 

How  many  square  inches  can  YOU  make  of  it? 

Draw  a  square  two  inches  on  a  side. 

Into  how  many  square  inches  can  you  cut  it? 


8      9 


0     II      12 


10.  This  is  a  picture  of  a  ruler  reduced  in  size. 

Here  is  a  real  foot-rule.     It  is  a  foot  long. 

Use  the  rule  to  find  how  long  this  table  is. 

How  many  feet  wide  is  the  table? 

Measure  this  line  on  the  blackboard.     How  long  is  it? 

What  is  the  length  of  this  blackboard? 

Cut  a  strip  of  paper  an  inch  long. 

Find  how  many  strips  are  as  long  as  the  foot-rule. 

There  are  twelve  inches  in  a  foot. 


The   Numbers    One   and   Two. 


11.    How  many  dots  are  on  the  first  card? 
Hold  up  one  finger.     Hold  up  one  more  finger. 
How  many  fingers  are  you  holding  up? 
How  many  fingers  are  one  finger  and  one  finger? 
Show  me  two  hands.     Show  me  two  buttons* 
Two  boys  are  how  many  more  than  one  boy? 


THE    NUMBER    THREE. 


Here  is  a  square.  [H    Make  pictures  of  two  squares. 

How  many  stars  are   ^  and  *fa  ? 

How  many  books  are  one  book  and  one  book? 

How  many  are  one  and  one? 

Here    are    two    squares.  []  Q  Push  away  the  one  on 
the  right.     How  many  are  left? 

Make  two  marks  on  the  board.     Rub    out    one    mark. 
How  many  are  left? 

One  marble  from  two  marbles  leaves  how  many  marbles  ? 

How  many  more  cents  are   @  ^p  than  ^p    ? 

How  many  cents  must  be  put  with  one  cent  to  have 
two  cents? 

/\  and    /\  are  how  many  triangles? 

O  and  O   are  how  many  circles? 

•  from  *   leaves  how  many  dots? 

and  -       -  are 


How  many  ones  in  two? 


The  Number  Three. 


12.  How  many  dots  are  two  dots  and  one  dot? 

]\lake  the  three  dots  on  the  board. 

Show  me  three  books.     Three  fingers. 

Say  school  three  times. 

How  many  sides  has  this  triangle?      /\ 


8  SCHOOL    ARITHMETIC. 

What  number  comes  before  three?     Before  two? 

What  number  is  between  one  and  three? 

How  many  rings  are   O   O   and    O  $ 

How  many  stars  are   ^f  and  ^  ^  ? 

How  many  cows  are  two  cows  and  one  COWT? 

I  have  one  cube.     Give  me  enough  to  make  three. 

Here  are  three  dots.    •   •   •     Cover  one  dot.   How  many 
are  not  covered? 

Cover  two  dots.     How  many  can  you  see? 
_  |||  p|  from  p|  |H|  |p|  leaves  how  many  flags  \ 

^A^.  ^A^.  ^fci.    ^ess  </fc>.  are  ^10W  many  tents  £ 
Measure  this  yardstick  with  your  foot-rule.     How  long 
is  it? 

13.  How  many  ones  in     J*  ? 
How  many  twos  in     J  J  ? 

How  many  pairs  of  twros  in     JJ  JJ  ? 
Show  me  two  threes,  using  splints. 
Show  me  three  twos  with  splints. 
Make  pictures  of  three  groups  of  stars. 
Make  pictures  of  three  pairs  of  tents. 

14.  Copy  and  complete: 
A  /\  o/rbd  /\ 


omxi^ 


O    O    O    llAA;    O    O    CtA^,   -- 


THE    NUMBER    FOUR.  9 

15.   Two  dogs  and  one  dog  are  how  many  dogs? 

One  foot  and  two  feet  are  -     -  feet. 

There  were  three  birds  on  the  fence,  but  one  flew  away. 
How  many  were  left? 

Mary  had  three  pennies,  but  now  she  has  only  two.  How 
many  did  she  spend? 

My  hat  cost  three  dollars.  I  have  paid  one  dollar;  how 
much  do  I  owe? 

Tom  ate  one  apple  and  had  two  left.  How  many  had 
he  at  first? 

Charles  has  three  rabbits,  and  Paul  has  one  less.  How 
many  has  Paul? 

The  Number  Pour. 


16.  Make  a  triangle  Avith  these  three  splints. 
Now  try  to  make  a  square  with  them. 
How  many  more  splints  do  you  need? 
How  many  dots  are  on  the  card  to  the  right? 
How  many  sides  has  a  square  ? 
How  many  seasons  in  the  year? 
Tell  me  the  names  of  four  boys. 
How  many  letters  in  the  word  four? 
Take  two  cubes  in  each  hand.     How  many  cubes  have 
you? 


10  SCHOOL   ARITHMETIC. 

How  many  triangles  can  you  make  with  these  twelve 
splints  ? 

I  have  one  cube.     Give  me  enough  to  make  four. 

If  I  give  you  one,  how  many  will  I  have  left? 

Cover  two  of  the  dots  on  the  right-hand  card.  How 
many  can  you  see? 

Show  me  the  number  of  splints  these  words  stand  for: 
three,  two,  four. 

Copy  these  pictures,  and  write  under  each  group  the 
word  for  the  number  (how  many)  in  each  group: 

#     nnnn     oo     AAA 


17.   How  many  tops  are  and 

How  many  marbles  are  ^)  and 
How  many  cents  are    ^p  ^p    and 
Q)   from   (^  Q^  (^  (^  leaves  how  many  apples? 
O   O   O   O   IGSS   O   O  are  now  many  circles? 
There  are  four  splints.     Give  me  half  of  them. 
How  many  have  I?    How  many  have  you? 
This  line  -         —  '  -  is  one  inch  long. 
In  one  inch  there  are  -  half  inches. 
This  line  -    -  '—  -  1  -  '—         -  is  two  inches 
long. 

In  two  inches  there  are  -  half  inches. 

In     fj     there  are     Q  M      (half  -circles). 
In  two  circles  there  are  -  half-circles. 


THE    NUMBER    FOTJK.  11 

18.  How  many  ones  in   J  J  ?    How  many  twos  ? 
Show  me  four  twos  with  splints. 

^lake  pictures  of  four  pairs  of  tents. 

Here  are  four  tops.  ^  ^  ^  ^  How  many  boys 
can  have  one  top  each? 

Here  are  four  pears.  (^  ^3  &  &  How  many  girls 
can  have  two  pears  each? 

Cut  a  strip  of  paper  three  inches  long. 

Find  how  many  strips  are  as  long  as  your  foot-rule. 

Cut  a  strip  of  paper  four  inches  long  and  one  inch  wide. 

Find  how  many  square  inches  will  cover  it. 

Ask  your  papa  how  many  quarters  make  a  dollar. 

Ask  your  mamma  how  many  quarts  in  a  gallon. 

19.  Copy  and  complete,  then  read: 

LJLJ  ED  o/nxL  CH  oA/t/ . 

O    aW,   O   O   O   ct/be,  -     -. 
i^^iZ  aW,  -        -  o/u, 
A  A  A  A  te^fc,  A  a/bo 


20.  Three  boys  and  one  boy  are  how  many  boys? 
One  tree  and  three  trees  are  how  many  trees? 
Two  sheep  and  two  sheep  are  -      -  sheep. 


12  SCHOOL    ARITHMETIC. 

Harry  had  four  apples,  but  gave  one  to  May.  How 
many  had  he  left? 

You  have  four  fingers  on  one  hand.  If  two  were  cut 
off,  how  many  would  you  have  left  on? 

Alice  had  four  kittens,  but  three  of  them  died.  How 
many  has  she  left? 

How  many  ears  have  two  rabbits? 

How  many  boys  have  four  heads? 

How  many  bicycles  have  as  many  wheels  as  a  wagon? 

The  Number  Five. 


21.  How  many  dots  on  the  left-hand  card? 

How  many  more  are  on  the  other  card? 

How  many  fingers  on  your  left  hand? 

How  many,  counting  the  thumb? 

Tell  me  the  names  of  five  boys. 

How  many  cents  is  a  nickel  worth? 

What  number  follows  four? 

What  number  is  between  three  and  five? 

I  have  four  beans.     Give  me  enough  to  make  five. 

Take  three  blocks.    Now  take  enough  more  to  make  five. 

Take  five  beans.    Separate  them  into  two  piles,  thus: 


Two  beans  and  three  beans  are  how  many  beans? 


THE    NUMBER    FIVE.  13 

Take  one  bean  from  the  smaller  pile  and  put  it  into 
the  larger. 

'Now  what  two  numbers  make  five? 

Here  are  five  rings.  O  O  O  O  O  Cover  one  of 
them.  How  many  are  not  covered? 

Cover  two  of  them.     How  many  can  you  see? 

Ask  your  papa  how  many  nickels  make  a  quarter. 

22.  How  many  ones  in  J«J  ? 
Show  me  two  fives  with  beans. 
Show  me  five  twos  with  beans. 


I 


ABC 

By  how  many  squares  is  D  larger  than  C?     Than  B? 
Than  A? 

A  and  B  together  are  as  large  as . 

How  can  we  make  C  as  large  as  D? 

Take  one  square  from  D  and  put  it  with  B. 

B  is  now  as  large  as  -     -  or  -    — . 

Draw  a  line  five  inches  long  on  paper. 

Draw  a  line  five  feet  long  on  the  blackboard. 


14  SCHOOL    ARITHMETIC. 

23.  Copy  and  complete,  then  read: 

O  O  O  O   o/rbd   O   o/u,  -     —  . 
A  A  A  CLmxL  A  A  o/u,  -      -. 


a/ue, 


(Q/vu, 


24.   Four  dolls  and  one  doll  are  how  many  dolls? 

One  finger  and  four  fingers  are  -      -  fingers. 

How  many  splints  will  make  a  triangle  and  a  tent,  if 
the  tent  is  made  like  this  A  • 

Sam  had  five  cents.  He  spent  one  cent  for  candy.  How 
many  has  he  left? 

Fred  had  five  marbles  and  lost  four.  How  many  has 
he  left? 

We  have  school  five  days  each  week.  If  you  stay  at 
home  two  days,  how  many  days  do  you  come  to  school? 

Ned  had  five  chickens.  The  cat  killed  three  of  them. 
How  many  has  he  left? 

If  your  papa  gives  you  a  cent  every  day,  in  how  many 
days  will  you  have  a  nickel. 

Jennie  bought  a  tablet  for  four  cents.  She  gave  the 
clerk  a  nickel.  How  many  cents  should  she  receive  back? 


THE    NUMBER    SIX. 


15 


The  Number  Six. 


25.  Here  are  .five  splints.  Make  a  triangle  and  then 
make  a  tent  like  this  /\. 

Can  you  make  two  triangles  with  the  same  splints? 

How  many  more  splints  do  you  need? 

How  many  dots  are  on  the  card  to  the  left? 

How  many  more  dots  are  on  the  other  card? 

Five  dots  and  one  dot  are  how  many  dots? 

Hold  up  six  fingers. 

Here  are  twelve  splints.  Make  as  many  tents  like  that 
above  as  you  can  with  them.  JsTow  count  them. 

What  number  follows  five?  What  number  comes 
before  six?  Before  five? 

I  have  five  cubes.     Give  me  enough  to  make  six  cubes. 

Take  six  blocks.     Put  four  in  one  pile,  two  in  another. 

Are  six  blocks  as  many  as  four  blocks  and  two  blocks? 

Now  arrange  the  six  blocks  in  two  equal  rows. 

How  many  are  in  each  row? 

Three  blocks  and  three  blocks  are  how  many  blocks? 

How  many  dots  are  here?  •••  |  •••  Cover  one  of 
them.  How  many  do  you  see? 


16  SCHOOL    ARITHMETIC. 

One  dot  from  six  dots  leaves  how  many  dots? 
Cover  two  of  them.    Tell  me  what  you  see. " 
Two  dots  from  six  dots  leaves  how  many  dots? 
Cover  three  dots.     How  many  can  you  see? 
Three  dots  from  six  dots  leaves  how  many  dots? 
How  many  dots  can  you  see  if  you  cover  four  of  them  ? 
Cover  five  of  them.    Tell  me  what  you  see. 
Copy  the  cards  below,  and  put  in  the  dots  needed  to 
make  six  dots  on  each  card. 


26.  How  many  twos  in  J  J  5   ?    How  many  threes? 

Show  me  two  sixes  with  cubes. 

How  many  cubes  have  you  used?  _ 

Cut  a  strip  of  paper  two  inches  long. 

How  many  strips  are  as  long  as  your  foot-rule? 

Cut  a  strip  of  paper  six  inches  long  and  one  inch  wide. 

Into  how  many  square  inches  can  you  cut  it? 

Draw  a  line  six  feet  long  on  the  blackboard. 

Measure  the  line  with  this  yardstick.  How  many  yards 
long  is  it? 

A  line  six  feet  ]ong  is  —  -  yards  long. 

Ask  your  mamma  how  many  eggs  there  are  in  a  half- 
dozen. 


THE    NUMBER    SIX.  17 

27.  Copy  and  complete,  then  read: 

o/uo     -  . 

n  n  c^^d,  n  a  a  a  ^    -. 

/  /  /    a/rbd  /  /  /   aA^  -  --  . 
•  •  •  •   a/nxL  -r—   -  a/u>   J  J  I  . 

O  O  O  O  O  O  f*A^  O  O 
AAAAAA 


A  A  A  A  A  A 


28.  How  many  days  in  a  week,  not  counting  Sunday? 

George  gave  me  five  roses  and  Ed  gave  me  one.  How 
many  did  I  then  have? 

One  pig  and  five  pigs  are  —  3  —  pigs- 

Robert  is  four  years  old.  How  old  will  he  be  in  two 
years  ? 

Two  bears  and  four  bears  are  how  many  bears? 

There  are  three  cows  on  each  side  of  a  fence.  How 
many  cows  are  there? 

Name  two  numbers  that  make  six.    Two  other  numbers. 

From  six  blocks  take  away  two  blocks.  How  many  are 
left? 

How  many  more  are  six  cents  than  one  cent? 

Then  what  two  pieces  of  money  make  six  cents? 

This  morning  I  had  six  apples,  Kow  I  have  only  three. 
How  many  have  I  eaten? 


18  SCHOOL   ARITHMETIC. 

What  part  of  them  have  I  eaten?  What  part  have  I 
left? 

Make  six  dots  on  your  slate.  Put  a  ring  around  one- 
half  of  them. 

One-half  of  six  dots  is  —  -  dots. 

Ask  your  papa  how  many  cents  will  pay  for  three  two- 
cent  stamps. 

The  Number  Seven. 


29.  Make  two  A/s  with  these  six  splints. 
Can  you  make  a  triangle  and  a  square  with  the  same 
six  splints?     Why  not? 

How  many  more  splints  do  you  need? 
Six  dots  and  one  dot  are  how  many  dots? 
Show  me  seven  dots.     Seven  cubes. 
Copy  these  cards: 


I  want  you  to  make  each  card  have  seven  dots. 
Name  two  numbers  that  together  make  seven.     Two 
other  numbers. 

Here  are  four  blocks.     Add  enough  to  make  seven. 
Now  take  two  away.     How  many  remain? 


THE    NUMBER    SEVEN.  19 

Here  are  one-cent,  two-cent,  three-cent,  four-cent,  and 
five-cent  postage  stamps.  Pick  out  any  two  that  you  can 
buy  with  seven  cents. 

30.  Make  pictures  of  seven  tents. 

Draw  a  line  around  three  of  them.  How  many  are 
outside  ? 

Show  me  two  sevens  with  dots. 

Cut  out  a  strip  of  paper  seven  inches  long  and  one  inch 
wide. 

Into  how  many  square  inches  can  you  cut  it? 

Draw  a  line  one  inch  long.  Close  to  the  right  end  draw 
a  line  six  inches  long. 

Xow  draw  a  line  below  them  as  long  as  both. 

How  many  inches  long  is  this  line? 

This  line  -  -  is  two  inches 

long.  How  much  longer  is  a  seven-inch  line? 

31.  Copy  and  complete: 

O  O  O  O  O   oWy   O  O   o/u,  --  . 


nnnnnnn  ^^  an  ***    -. 

AAAAAAAf^--     -  a/u,  AA- 


20 


SCHOOL    ARITHMETIC. 


32.  How  many  days  in  a  week? 

Name  the  days  of  the  week,  beginning  with' Sunday. 

The  middle  of  the  week  is  "W . 

On  Wednesday  morning  how  many  days  of  the  week 
are  gone?  How  many  are  left? 

How  many  sides  have  a   /\    and  a  |    |  ? 

Five  girls  and  two  boys  went  out.     How  many  are  out? 

When  one  comes  in,  how  many  will  be  out? 

Each  week  we  come  to  school  five  days  and  stay  at 
home  -  -  days. 

Joe  had  seven  cakes.  The  cat  took  three  of  them.  How 
many  had  he  left? 

Here  are  seven  apples.  OOOOOOO  Name 
each  number  of  apples  that  you  can  take  away,  and  tell 
how  many  will  remain. 

The  Number  Eight. 


33.  Make  a  triangle  and  a  square  with  splints.  How 
many  splints  have  you  used? 

Try  to  make  two  squares  with  the  splints. 

How  many  more  splints  must  you  have  ? 

Seven  splints  and  one  splint  are  how  many  splints? 

Show  me  eight  dots.  Show  me  eight  buttons.  Point 
to  eight  corners  in  this  room, 


THE    NUMBER    EIGHT.  21 

Make  a  pile  of  eight  blocks. 

Now  make  two  piles  of  them,  putting  the  same  number 
in  each.     How  many  in  each  pile? 
.    Four  blocks  and  four  blocks  are  how  many  blocks? 

Take  a  block  from  one  pile  and  place  it  on  the  other. 
Xow  how  many  in  each  pile? 

Five  blocks  and  three  blocks  are  how  many  blocks? 

Take  another  block  from  the  smaller  pile  and  place  it 
on  the  larger.     How  many  in  each  pile? 

Six  blocks  and  two  blocks  are  how  many  blocks? 

Name    two    numbers    that    make    eight.     Two    other 
numbers.     Who  can  name  still  two  other  numbers? 

What    number    comes    before    eight?      Before    seven? 
Before  six?     Before  five? 

What  number  is  between  five  and  seven?    Between  six 
and  eight? 

A  nickel  and  how  many  cents  make  eight  cents? 

Copy  these  blank  cards,  and  put  in  each  the  number  of 
dots  indicated  by  the  word  written  under  it: 


eight  six  seven  five  four  three 

34.  Make    four    dots,  thus:  J  2  •    Draw  a  line  around 
one-half  of  them. 

Into  how  many  equal  parts  have  you  divided  them? 
One-half  of  four  dots  is dots. 


22  SCHOOL    ARITHMETIC. 

Make  eight  clots,  thus:    I  I  Z  J  • 

Draw  a  square  around  one-half  of  them.  Draw  a  line 
around  the  other  half. 

One-half  of  eight  dots  is  dots. 

Show  me  one-half  of  six  dots. 

How  many  squares  are  there  here? 

What  part  of  them  is  black? 

Four  squares  are  one-half  of  -       -  squares. 

How  much  of  this  circle  is  black? 

A  dollar  is  worth  how  many  half-dollars? 

Find  by  trial  to-night  how  many  quarts  in  a  half-gallon. 

35.  How  many  fours  in    5  •  I  •   •    How  many  twos? 

Show  me  eight  shoes.     How  many  pairs  are  there? 

Draw  four  rings  above  a  line,  and  four  below  it.  How 
many  times  did  you  draw  four  rings? 

Draw  a  line  around  one-half  of  the  rings.  How  many 
rings  are  inside  of  the  line? 

Make  pictures  of  eight  tents,  four  in  a  row.  Cross 
out  one-half  of  them.  How  many  are  left? 

Make  pictures  of  eight  stars,  two  in  a  row.  How  many 
rows  have  you? 

Make  pictures  of  one-half  of  eight  squares. 

Tell  all  you  can  about  these  figures. 


Two  horses  need  -       -  pairs  of  shoes.     In  four  pairs 
there  are  -      -  shoes. 

The    spider    has  -      -  legs.     How  many  pairs  of  legs 

does  the  spider  have? 


THE    NUMBER    EIGHT.  23 

36.  Copy  and  complete: 

A  A  A  A  A  ci/YuL  A  A  A  o/u,  -  . 

•    •••••     CX/YbcL    --    OJ\JL>     •    •    •    •  • 

X   X   X    X    a/Ybd    X    X    X    X 

'///////    O/YUL   / 


• 


37.  Seven  bugs  and  one  bug  are  how  many  bugs? 

One  bean  and  seven  beans  are  -      -  beans. 

A  man  has  six  white  sheep  and  two  black  sheep.  How 
many  sheep  has  he? 

There  are  five  eggs  in  a  dish.  We  need  eight  for  dinner. 
How  many  more  must  we  find? 

Mr.  Jones  has  eight  horses  in  two  fields.  There  are 
four  in  one  field.  How  many  are  in  the  other  field? 

Eight  birds  were  sitting  on  a  fence.  A  bad  boy  shot 
one.  How  many  were  left? 

A  boy  had  two  fingers  cut  off.    How  many  were  left  on? 

We  have  two  gallons  of  milk.  How  many  quarts  have 
we?  Find  by  trial. 

DrawT  a  figure  four  squares  long  and  two  squares  wide. 

This  figure  contains  -      -  squares. 


SCHOOL    ARITHMETIC. 


The  Number  Nine. 


38.  Make  two  squares  with  splints.     How  many  splints 
have  you  used? 

Try  to  make    three   triangles    with    the    splints.     How 
many  more  splints  do.  you  need? 

How  many  more  than  eight  dots  are  on  the  card  to  the 
right? 

Eight  dots  and  one  dot  are  how  many  dots? 

Take  nine  blocks  and  lay  them  in  a  row. 

Push  one  away.    How  many  are  left? 

One  block  and  eight  blocks  are  how  many  blocks? 

One  block  from  nine  blocks  leaves  how  many  blocks? 

If  you  push  three  blocks  away,  how  many  will  be  left? 

Take  away  all  but  two.     How  many  have  you  taken? 
/Lay  the  nine  blocks  in  three  rows,  three  in  a  row. 
I  Now  tell  me  how  many  threes  make  nine. 

Copy  these  cards: 


Add  enough  dots  to  make  each  card  have  nine. 
Name  two  numbers  that  together  make  nine.    Two  other 
numbers. 


THE    NUMBER    NINE. 


How  many  splints  will  make  three  triangles? 

Draw  a  square  like  this: 

How  many  of  the  nine  small 
squares  are  white? 

Make  another  black.     Two  black  squares  and  

white  squares  are  nine  squares. 

Cut  out  a  paper  triangle  three  inches  on  a  side.     How 
long  are  all  the  sides? 

Copy  these  squares,  and  put  in  each  square  the  number 
of  dots  indicated  bv  the  word  written  under  it : 


none 


four 


six 


eight 


nine 


39.  There  are  eight  pigs  in  the  pen  and  one  on  the 
road.  How  many  pigs? 

The  white  hen  has  seven  chicks,  the  black  hen  has  two. 
How  many  chicks? 

There  are  six  eggs  in  one  nest  and  three  in  another. 
How  many  eggs  in  both  nests? 

Five  boys  and  four  girls  are  how  many  children? 

Dan  has  three  pennies,  Nell  has  three,  and  Kate  has 
three.  How  many  have  they  all? 

Nine  sheep  were  in  a  field,  but  one  jumped  out.  How 
many  were  left  in? 


26  SCHOOL    ARITHMETIC. 

Here   are  nine   tents, 


If  the  wind  blows  two  down,  how  many  will  remain 
standing? 

If  I  take  three  of  them  away,  how  many  will  be  left? 

How  many  times  can  you  take  three  tents  away? 

If  a  book  costs  nine  cents,  it  will  take  a  nickel  and— 
pennies  to  pay  for  it. 

This  line  on  the  blackboard  is  nine  feet  long.     Find 
how  many  yards  long  it  is. 

The  Number  Ten. 


40.  How  many  fingers  and  thumbs  have  you?  How 
many  more  than  nine? 

Make  a  pile  of  ten  blocks. 

How  many  cents  is  this  dime  worth? 

Copy,  and  add  dots  enough  to  make  ten  dots  on  each 
card: 


Make  eight  tents  and  two  tents.     How  many  have  you 
made? 

Make  seven  stars  and  three  stars.     How  many? 


THE    NUMBER    TEN.  2 

Draw  six  rings  and  four  rings.     How  many  rings? 

Five  fingers  and  five  fingers  are  how  many  fingers? 

How  many  dots  on  the  right-hand  card? 

How  many  fives  do  you  see  on  it? 

How  many  nickels  make  a  dime? 

How  many  tents  can  you  make  with  ten  splints,  if  the 
tents  are  made  like  this  /\  ? 

Xame  two  numbers  that  make  ten.    Two  other  numbers. 

Lay  ten  blocks  in  a  row.  Push  one  away.  How  many 
are  left? 

If  you  take  two  away,  how  many  will  be  left? 

Two  blocks  from  ten  blocks  leaves  hoAV  many  blocks  ? 

Draw  a  square.  Make  ten  dots.  Now  put  one  half  of 
the  dots  inside  the  square. 

One-half  of  ten  dots  is  how  many  dots? 

Make  two  piles  of  ten  blocks  each.     How  many  tens? 

Two  tens  and  three  tens  are  how  many  tens? 

Nine  fives  and  one  five  are  how  many  fives? 

Use  dots  to  show  me  three  twos. 

Four  twos  and  one  two  are  how  many  twos? 

Show  me  five  twos  with  dots.     How  many  ones? 

How  many  fingers  have  two  boys? 

How  many  clocks  have  ten  hands? 

Find  whether  this  room  is  ten  yards  long. 

How  many  feet  less  or  more? 

41.  Willie  had  nine  cents  and  his  uncle  gave  him  one 

more.     He  then  had cents,  or  one . 

How  many  children  are  eight  boys  and  two  girls? 


Ao  SCHOOL    ARITHMETIC. 

A  week  and  three  days  are  how  many  days  ? 

This  line  on  the  blackboard  is  ten  inches  long,  and  this 
one  is  nine  inches  long.  How  much  longer  is  one  than 
the  other? 

Dan  had  ten  cents.  He  spent  two  cents  for  a  pencil. 
How  many  cents  had  he  left? 

A  man  had  three  of  his  toes  cut  ofT.  How  many  were 
left  on? 

Bessie  started  to  the  store  with  ten  cents  (two  nickels), 
but  lost  one-half  of  her  money.  How  much  had  she  left? 

How  many  two-cent  stamps  are  worth  a  dime  ? 

If  you  have  ten  cents,  how  often  can  you  spend  five 
cents  ? 

If  one  orange  costs  five  cents,  how  much  money  will  be 
needed  to  buy  two  oranges? 


The  Numbers  Eleven  and  Twelve. 


42.  How  many  dots  are  on  the  left-hand  card?     How 
many  more  than  ten? 

Ten  dots  and  one  dot  are  how  many  dots? 
A  dime  and  a  penny  are  how  many  cents? 


THE    NUMBERS    ELEVEN    AND    TWELVE.  29 

Here  is  one  block.  Put  enough  more  here  to  make 
eleven. 

Kame  two  numbers  that  make  eleven.  Two  other 
numbers. 

Make  two  squares  and  a  triangle  with  splints.  How 
many  splints  have  you  used? 

Try  to  make  three  squares  with  the  same  splints.  How 
many  more  do  you  need ? 

Eleven  splints  and  one  splint  are  how  many  splints? 

Make  a  pile  of  twelve  blocks. 

Xow  take  two  blocks  away.    How  many  are  left? 

Twelve  blocks  are  how  many  more  than  ten  blocks? 

How  many  dots  do  you  see  here?     !!!!!! 

How  many  sixes  in  twelve?  How  many  twos?  How 
many  fours? 

Cut  a  strip  of  paper  six  inches  long.  How  many  strips 
are  as  long  as  your  foot-rule? 

How  many  six-inches  in  twelve  inches? 

Find  how  many  strips  each  four  inches  long  are  as  long 
as  your  ruler. 

How  many  four-inches  make  twelve  inches?  How  many 
two-inches? 

Make  twelve  tents  with  splints.  Let  the  wind  blow 
down  one-half  of  them.  How  many  are  left? 

43.  Twelve  boys  are  how  many  more  than  eleven  boys? 
There  are  ten  eggs  in  a  nest.     When  the  hen  lays  two 
more  there  will  be  -     -  eggs  in  the  nest. 


30  SCHOOL    ARITHMETIC. 

My  two  horses  ate  twelve  ears  of  corn.  The  gray  horse 
ate  six  ears.  How  many  ears  did  the  bay  horse' eat? 

Mamma  bought  a  dozen  oranges  at  the  store.  We  ate 
six  for  breakfast.  How  many  were  left? 

I  found  a  nest  with  twelve  eggs  in  it.  I  took  out  all 
but  one.  How  many  did  I  take? 

Twelve  of  Mr.  Smith's  sheep  were  sick.  Two  of  them 
died.  How  many  got  well? 

Six  boys  were  playing  soldiers  on  one  side  and  five  on 
the  other.  How  many  boys  were  there  altogether? 

Henry's  father  gave  him  a  dozen  pencils.  How  many 
had  he  left  after  using  four? 

Marvin  has  a  five-cent  piece  and  three  pennies.  How 
many  more  cents  must  he  have  to  pay  for  a  top  worth 
eleven  cents? 

Harry's  knife  has  two  blades.  How  many  blades  do  six 
such  knives  have? 

We  learned  five  new  words  yesterday.  If  we  learn  one 
more  to-day  than  Ave  did  yesterday,  how  many  have  we 
learned  in  both  days? 


PRIMARY   NUMBER   WORK. 


44.  How  many  ones  on  the  middle  card?     How  many 

twos? 

Two  dots  are  how  many  more  than  one  dot? 
Three  dots  are  how  many  more  than  two  dots? 
How  many  dots  on  the  first  two  cards? 
Cover  two  of  the  dots  on  the  last  card.     How  many  do 
you  see? 

One  dot  and  one  dot  are  -      -  dots. 

Two  tents  and  one  tent  are  —   -  tents. 

One  square  and  two  squares  are  -      -  squares. 

Two  stars  less  one  star  are  -     -  star. 

Three  tents  less  one  tent  are  -      -  tents. 
Make  pictures  of: 

Two  stars  and  one  star  are  three  stars. 

One  tent  and  two  tents  are  three  tents. 

Three  dots  less  one  dot  are  two  dots. 

Three  rings  less  two  rings  are  one  ring. 

How  many  ones  in  two?    In  three?    What  two  numbers 
make  three? 

[31] 


32  SCHOOL    ARITHMETIC. 

Make  the  figure  that  stands  for  the  number  one  —  • 
Make  the  figure  that  stands  for  the  number  two  — 
Make  the  figure  that  stands  for  the  number  three  — 
Use  figures  instead  of  these  pictures  : 


less 

D  D  D  iess  D  D  are  Q- 
2  dots  and  1  dot  are  -     -  dots. 

1  star  and  1  star  are  -     -  stars. 

2  tents  less  1  tent  are  -     -  tent. 

3  cents  less  1  cent  are  -     -  cents. 

3  squares  less  two  squares  are  -     -  square. 

45.    Here  are  some  squares: 

n  i 

DP    a 
ODD    3 

Write  the  figure  for  the  number  of  squares  in  the 
upper  row. 

Under  this  write  the  figure  for  the  number  of  squares 
in  the  second  row. 

One  square  and  two  squares  are  -  squares. 

Write  3  under  the  2  with  a  line  between.  Is  3  the 
number  of  squares  in  both  upper  rows? 

Three  squares  is  the  sum  of  one  square  and  two  squares. 

Finding  the  sum  of  two  or  more  numbers  is  called 
adding. 


NUMBERS    1    TO    3. 

Add  these  numbers: 


33 


DD 


nn 


Take  one  square  from  3  squares.     How  many  are  left? 
Taking  one  number  from  another  is  called   subtracting. 


Subtract  the  following: 

2  3 

1  1 


46.    Add: 

1  foot 

2  feet 


2  cents 
1  cent 


1  yard 
1  yard 


Subtract: 

2  feet 
1  foot 

3  yards 
1  yard 

3  cents 
2  cents 

2  tops 
2  tops 

Complete  : 

1  and  1  are  (     ).     2  less  1  are  (     ).    3  less  2  are  (     ). 


2  and  1  are  (     ).     2  and  (     )  are  3. 
1  and  2  are  (     ).     3  less  1  are  (     ]. 


3  less  (     )  are  2. 
3  less  (     )  are  1. 


34  SCHOOL    ARITHMETIC. 

47.  Make  a  picture  for  2  and  1  are  3.     (J  and  •  are  J0). 
Tell  a  story  about  1  and  1  are  2. 

ANS.— My  dolly  had  1  dress,  and  I  made  her  1  more.     She  then 
had  2  dresses. 

Tell  a  story  about  1  and  2  are  3. 

Emma  has  two  pairs  of  shoes,  and  Lillie  has  one  pair. 
How  many  pairs  have  they  both? 

Mary  had  three  dimes,  but  lost  one.  How  many  had 
she  left? 

Tell  another  story  about  3  less  1  are  2. 

My  hat  cost  two  dollars.  I  have  paid  one  dollar.  How 
much  do  I  owe  ? 

We  have  three  quarts  of  milk  for  sale.  How  many 
times  can  we  sell  one  quart? 

Then  how  many  quarts  are  3  times  1  quart? 

How  many  fives  are  one  five  and  two  fives? 

Clara  ate  one  peach,  and  has  two  left.  How  many  had 
she  at  first? 

John  had  three  marbles  and  gave  one  to  Sam.  Ask  a 
question  and  answer  it. 

Here  are  3  pears.  &  (^  &  How  many  boys  can 
each  have  1  pear? 

How  many  ones  in  3? 

Count  forwards  to  three,  then  backwards  to  one. 

Tell  me  some  things  you  have  learned  about  the  number 
three, 


FOUR — 4.  35 


Four 


48.  How  many  ones  are  pictured  on  this  card?  How 
many  twos? 

Four  dots  are  how  many  more  than  three  dots?  How 
many  more  than  two  dots? 

Name  two  numbers  whose  sum  is  four.  Two  other 
numbers. 

Show  with  splints  that  your  answers  are  correct. 

Here  are  four  tents.  Cover  one.  How  many  are  not 
covered  ? 

If  two  tents  were  taken  away,  how  many  would  be  left? 

How  many  times  can  one  tent  be  taken  away? 

Then  four  times  one  tent  are  -      -  tents. 

Here  are  four  blocks.  Eva  may  take  two  blocks.  Now 
she  may  take  two  more. 

How  many  times  has  she  taken  two  blocks?  -How 
many  blocks  has  she? 

Then  two  times  two  blocks  are  blocks. 

Show  with  pegs  that  two  twos  are  as  many  as  four  ones. 

Here  are  four  cents.  ^p  (gP  (QP  How  many 

girls  can  have  one  cent  each?  How  many  ones  in  four? 

How  many  boys  can  have  two  cents  each?  How  many 
twos  in  four? 


36  SCHOOL    ARITHMETIC. 

49.  Separate  four  blocks      ^^ 
into  two  equal  parts,  thus: 

What  is  one  part  called? 

What  must  you  do  with  an  apple  to  get  one-half  of  it? 
(Divide  it  into  two  equal  parts.) 

What  must  you  do  with  four  blocks  to  find  one-half  of 
them? 

If  anything  is  divided  into  two  equal  parts,  what  is 
one  of  the  parts  called? 

In  an  apple  there  are  —     -  half -apples. 

How  many  halves  make  a  whole  pie? 

One  half  from  two  halves  leaves  -      -  half. 

Draw  two  squares  and  divide  them  into  halves. 

In  two  squares  there  are  -      -  half-squares. 

We  write  one-half  thus:  \. 

Two  blocks  are  J  of  -      -  blocks. 

Write  the  figure  that  stands  for  the  number  four  - 

50.  The  sign  +  stands  for  and.     Copy  the  following, 
using  +  instead  of  and: 

1  and  1  are  2.  3  and  1  are  4. 

2  and  1  are  3.  2  and  2  are  4. 

Kead  these: 

1  +  2  are  3.  1  +  3  are  4. 

1  +  1  are  2.  2  +  2  are  4. 


FOUR  —  4.  37 

The  sign  —  stands  for  less.     Copy  the  following,  using 
—  instead  of  less: 

2  less  1  are  1.  3  less  2  are  1. 

3  less  1  are  2.  4  less  1  are  3. 

Read  these: 

3  —  1  are  2.  4  —  2  are  2. 

3  —  2  are  1.  4  —  3  are  1. 

We  may  use  the  sign  =  for  are. 

Read  these: 

2  +  2  =  4.         4—2  =  2. 


Copy  and  complete: 


1  +  3  =  ().  l  +  ()  =  4.  4-l  =  O. 

2  +  2  =  (  ).  2  +  O_  =  4.  *  —  3  =  (  ). 
4  =  3  +  O-  4-()  =  3.  4-()  =  2. 
4-1  +  O-  4-O  =  l.  4  =  2  +  O. 

NOTE.  —  To  secure  facility  on  the  part  of  the  pupils  the  teacher 
should,  as  often  as  may  be  found  necessary,  require  them  to  an- 
nounce results  at  ftiyJit.  He  should  also  train  them  to  give  answers 
immediately  upon  hearing  the  numbers  and  operations  named. 
This  applies  to  all  exercises  involving  the  "  combinations." 


38  SCHOOL    ARITHMETIC. 

51.     Make  a  picture  for  2  +  2  =  4. 


How  many  boys  together  have  as  many  legs  as  a  horse? 

George  earned  one  quarter  on  Monday  and  three 
quarters  on  Tuesday.  How  much  did  he  earn  in  both  days  ? 

Ask  your  papa  how  many  quarters  there  are  in  a  dollar. 

Tell  a  story  about  8  +  1  ==  4. 

I  bought  four  pounds  of  meat.  Two  pounds  of  it  was 
pork  and  the  rest  beef.  Ask  a  question  and  answer  it. 

Charlie  has  four  rabbits  and  Paul  has  one  less.  How 
many  has  Paul? 

How  many  more  fingers  than  thumbs  has  your  hand  ? 

Count  from  one  to  four;  then  count  from  four  back 
to  one. 

If  one-half  of  a  lemon  is  worth  two  cents,  how  much  is 
the  lemon  worth? 

If  a  cake  is  worth  four  cents,  how  much  is  one-half  of 
it  worth? 

One  half-dollar  and  one  half-dollar  are  -  . 


PINT  QUART  GALLON 

52.  Which  of  these  measures  is  the  largest?  Which 
is  the  smallest? 

Fill  each  measure  with  water,  then  tell  me  which  is 
the  heaviest. 


FOUR  —  4.  39 

The  gallon  measure  is  full  of  water.  Find  how  many 
times  it  will  fill  the  quart  measure. 

Find  how  many  times  you  can  fill  the  quart  measure 
and  empty  it  into  the  gallon  measure. 

One  gallon  is  as  much  as  -      -  quarts. 
4  quarts  make  1  gallon. 

Mabel  had  a  gallon  of  milk,  but  fell  and  spilled  a  quart. 
She  had  quarts  left. 

Papa  brought  home  a  gallon  of  oil  in  a  can.  There  is 
only  one  quart  in  it  now.  How  much  has  been  used? 

Fill  the  pint  measure  and  empty  it  into  the  quart 
measure.  How  many  times  must  you  do  this  to  fill  the 
quart  measure? 

One  quart  is  as  much  as  -     -  pints. 

2  pints  make  1  quart. 

A  pint  is  what  part  of  a  quart? 

Two  quarts  are  what  part  of  a  gallon? 

When  milk  is  two  cents  a  pint,  how  much  does  a  quart 
cost? 

Jennie  paid  four  cents  for  a  quart  of  vinegar.  How 
much  did  a  pint  cost? 

Mamma  gave  four  quarters  for  a  gallon  of  molasses. 
How  much  did  a  quart  cost  ? 

Tell  a  story  about  a  quart  and  a  gallon. 

Tell  me  some  things  you  have  learned  about  the 
number  four. 


40  SCHOOL   ARITHMETIC. 


Five 


53.  How  many  dots  on  this  card?     Of  what  number 
are  they  a  picture? 

Without  the  one  in  the  center,  how  many  are  there? 

Cover  the  two  at  the  right.     How  many  can  you  see? 

Are  three  dots  and  two  dots  as  many  as  four  dots  and 
one  dot? 

Name  two  numbers  whose  sum  is  five.  Two  other 
numbers. 

What  number  is  one  less  than  five?    Two  less? 

Are  five  ones  as  many  as  one  five? 

Which  would  you  rather  have — five  pennies  or  a 
nickel?  Why? 

Count  these  squares,  beginning  ; it  the  left.    Q  |§5  [H  d  d 

Which  square  did  you  call  one?  Which  did  you  call 
two? 

Is  the  black  square  really  two  squares,  or  merely 
another  one  square? 

The  first  square  and  the  second  square  are  how  many 
squares? 

Make  the  figure  that  stands  for  the  number  five  —  J~. 

54.  Here  are  five  balls.     ®  ©©©(£) 

If  Owen  takes  1  ball  at  a  time  for  5  times,  how  many 
balls  will  he  have? 

Then  5  times  1  ball  are  how  many  balls? 


FIVE 5. 

5  times  1  are  how  many? 
Here  are  five  cents. 

How  many  boys  can  have  1  cent  apiece? 
How  many  ones  in  5  ? 
How  many  boys  can  have  2  cents  apiece? 
How  many  will -be  left  for  another  boy? 
Two  2's  and  1  are . 


-B 
C 


-E 


-D 


The  line  D  and  the  line  A  equal  which  line? 

The  line  B  and  the  line  C  equal  which  line? 

The  line  B  is  how  many  times  as  long  as  the  line  A? 

The  line  D  is  howr  many  times  as  long  as  the  line  B? 

If  from  the  line  E  we  take  a  line  equal  to  the  line  A, 
which  line  will  the  remainder  equal? 

Show  me  the  number  of  blocks  these  figures  represent: 
3,  5,  1,  4,  2. 

Now  make  the  figures  that  represent  the  number  of 
blocks  I  show  you.  (Show  blocks.) 

55.     Copy,  complete,  and  read: 

4  +  !-=().    5 —!=  =  ().    4  +  ()  =  5.  5  —  (  )  =  3. 

1  +  4  =  ().    5-4==().     3  +  ()  =  5.  5-()  =  2. 
3  +  2  =  ().    5  — 2— ().    5— (.  )  =  4.  5  =  4  +  (  ). 

2  +  3  =  ().    5—  3=().    5  —  ()  =  !.  5  =  2  +  (). 


42  SCHOOL    ARITHMETIC. 

56.    Make  a  picture  for  3  +  2  =  5. 

Four  little  toes  and  one  great  toe  are toes. 

My  hat  cost  three  dollars  and  my  shoes  two  dollars. 
How  much  did  both  cost? 

A  lady  bought  two  pounds  of  coffee  at  one  store  and 
three  pounds  at  another.  Ask  a  question  and  answer  it. 

2  pounds  4"  3  pounds  =  pounds. 

We  have  school  five  days  each  week.  If  you  stay  at 
home  two  days,  how7  many  days  do  you  come  to  school? 

Tell  a  story  about  5  —  4  ==  1. 

It  is  five  miles  to  Salem.  When  we  have  traveled 
three  miles,  how  far  have  we  yet  to  go  ? 

This  line  on  the  blackboard  is  one  foot  long,  and  this 
one  is  five  feet  long.  Tell  me  all  you  can  about  the  two 
lines. 

In   O   O   an(i  Dj   how  many  half-circles  are  there? 
For  a  nickel  I  can  buy  -      -  2-cent  stamps  and  - 
1-cent  stamp. 

Tell  some  other  things  you  can  buy  with  a  nickeL 
Helen,  please  tell  all  you  know  about  four. 

ANS. — 3  and  1  are  four,  2  and  2  are  four,  1  and  3  are  four ;  two  twos 
are  four  ;  4  less  1  are  three,  2  from  4  leaves  two,  etc.,  etc. 

James,  be  kind  enough  to  state  what  you  know  about 
five. 


six  —  6.  43 


Six  6 


57.    How  many  cents  can  you  get  for  a  nickel? 

If  I  should  give  you  one  more  penny,  how  many  cents 
would  you  have? 

Would  you  have  a  cent  for  every  dot  on  this  card? 

Show  me  five  fingers  and  one  finger.     How  many? 

Draw  a  line  four  inches  long.  At  one  end  of  it  draw 

a  line  two  inches  long.  Both  together  make  a  line  

inches  long. 

Here  are  six  tops.     ^    ^    ^    ^    ^    ^ 

If  Ben  takes  two  tops  at  a  time  for  three  times,  how 
many  tops  will  he  have? 

Then  how  many  tops  are  3  times  2  tops? 

Here  are  six  balls.      <££)  <£)  ©  I  ©  <£D  © 

Jack  may  take  3  balls;  then  3  more. 

How  many  times  has  Jack  taken  3  balls? 

Here  are  6  marbles.      Q  Q  Q  Q  Q  Q 

How  many  boys  can  have  1  marble  each? 

How  many  ones  in  6? 

How  many  boys  can  have  2  marbles  each? 

How  many  twos  in  six? 

How  many  boys  can  have  3  marbles  each? 

How  many  threes  in  six? 


44  SCHOOL  ARITHMETIC. 

How  many  threes  do  you  see  on  the  card?  Two  threes 
are  . 

How  many  twos  are  on  the  card  ?    Three  twos  are  -    — . 

Show  me  with  blocks  that  two  threes  are  as  many  as 
three  twos. 

Here  are  four  squares.  How  many 

more  must  we  draw  to  have  six? 

The  sum  of  five  and  one  is  six.  Name  two  other  num- 
bers whose  sum  is  six.  Two  others. 

Draw  a  line  six  inches  long  on  your  slate.  Rub  out 
one  inch  of  it.  How  long  is  the  remainder? 

If  two  dots  are  taken  from  six  dots,  how  many  dots  will 
remain  ? 

Make  the  figure  that  stands  for  the  number  six  —  <f. 
58.    Divide  6  dots  into  three  equal  parts  thus: 


How  many  dots  are  there  in  each  part? 
When  a  number  of  things  is  divided  into  three  equal 
parts,  each  part  is  one-third  of  the  whole  number. 

What  is  one-third  of  6  dots?     One-third  is  written  —  -?,. 
J  of  6  cents  is  -      -  cents. 

Into  how  many  equal  parts  is  the  first 
circle  divided?     The  second? 

What  part  of  the  first  circle  is  dark? 

What  part  is  light? 

How  much  of  the  second  circle  is  dark? 


six  —  6.  45 

Which  is  greater — one-half  or  one-third  of  anything? 

Two  thirds  of  a  pie  and  one  third  of  a  pie  are  how  much 
of  the  pie? 

Cut  this  apple,  giving  one-third  to  John,  one-third  to 
Charley,  and  keeping  one-third  yourself.  In  one  apple 
how  many  thirds  of  an  apple? 

Tii  2  apples  there  are  -      -  thirds  of  an  apple? 

59.  Copy,  complete  and  read: 

5  +  !  =  ().  3  +  8  =  O<  6  —  4  =  ().  2  +  ()  =  6. 

1  +  5==().  6-l  =  ().  6  — 3  =  ().  6-()  =  4. 

4  +  2  =  (  ).  6  —  5  =  (  ).  4  +  (  )  =  6.  1  +  (  )  =  6. 

2  +  4  =  ().  6  —  2  =  O-  6  —  ()  =  2.  Jof  6  =  O- 

3  +  (  )  =  6.  6  —  (  )  =  3.  i  of  6  =  (  ).  J  of  3  =  (  ). 

60.  Make  a  picture  for  3  +  3  =  6. 

Harry  made  five  rings  and  Stella  made  one.  How 
many  did  both  make? 

Maud,  you  may  draw  two  circles.  Annie  may  draw 
four.  How  many  have  both  drawn? 

The  black  cow  gives  a  gallon  of  milk,  the  red  cow  two 
quarts.  How  much  do  both  give? 

There  are  three  horses  on  each  side  of  a  fence.  How 
many  horses  are  there?  Draw  the  picture. 

Draw  a  line  two  yards  long.     How  many  feet  long  is  it? 

A  lady  who  had  six  dollars  gave  one  dollar  for  gloves. 
Ask  a  question  and  answer  it. 

A  man  had  six  ten-dollar  bills,  but  spent  two  of  them. 
How  many  had  he  left? 


46  SCHOOL    ARITHMETIC. 

Henry  gets  two  dollars  a  day.  How  much  does  he  earn 
in  three  days? 

Our  hens  lay  three  eggs  a  day.  How  many  do  they  lay 
in  two  days? 

A  man  gets  six  dollars  for  working  a  day.  How  much 
does  he  get  for  working  half  a  day? 

Tell  a  story  about  6  —  3  =  3. 

If  one  orange  costs  3  cents,  what  does  one-third  of  the 
orange  cost? 

If  one-third  of  a  melon  is  worth  2  cents,  what  is  the 
whole  melon  worth? 

Alice  has  one-half  of  6  cents  and  Frances  has  one-third 
of  6  cents.  Which  has  the  more  money? 

Who  wants  to  tell  me  all  about  six?    James  may  tell. 

Now  you  may  all  go  to  the  board  and  write  what  he  has 
told  us. 


Seven 


61.  Make  two  triangles  with  splints.  How  many  have 
you  used? 

Can  you  make  a  triangle  and  a  square  with  the  same 
splints?  How  many  more  do  you  need? 

Six  dots  and  one  dot  are  -     -  dots. 

How  many  days  in  a  week?     Name  them. 

Draw  a  line  six  inches  long,  and  another  one  inch  long. 
What  is  the  length  of  both  lines? 


SEVEN  7.  4:7 

Take  seven  blocks.  Take  two  of  them  away.  How  many 
are  left? 

Five  blocks  and  two  blocks  are blocks. 

Now  take  three  blocks  from  the  seven.  How  many  in 
each  pile? 

Cut  out  a  strip  of  paper  seven  inches  long.  Cut  off  an 
inch  from  one  end.  "What  is  the  length  of  the  part  left? 

This  line  on  the  blackboard  is  four  feet  long.  Make 
it  seven  feet  long.  How  long  is  the  line  you  have  drawn? 

Draw  a  line  seven  inches  long  on  the  blackboard.  Helen 
may  rub  out  one  inch  of  her  line.  How  long  is  the  part 
left? 

Tom  may  rub  out  two  inches  of  his  line.  How  much 
of  the  line  is  left? 

Hester  may  erase  three  inches  of  her  line.  Tell  me 
something  about  the  part  left. 

Xame  two  numbers  whose  sum  is  seven.  Two  other 
numbers. 

How  many  are  Q  Q  and  Q  Q  and  Q  Q  and  Q  ? 

Can  you  name  three  numbers  that  together  make  seven  ? 

Show  me  the  number  of  blocks  these  figures  stand  for: 
6,  7,  5,  4,  3. 

Make  the  figures  that  stand  for  the  number  of  balls  I 
hold  up. 

62.    Copy,  complete  and  read: 

6  +  l  =  ().  5  +  ()  =  7.  7-l  =  ().  7-3  =  (). 
5  +  2  =  O-  3  +  ()  =  7.  7-6  =  ().  7-4  =  O- 
4  +  3  =  -  l  +  =  7.  7  — 2  =  .  7-  =  5. 


4:8  SCHOOL   ARITHMETIC. 

Add  quickly: 

564123 

213654 

Subtract  at  sight: 

777777 
162534 

63.  You  come  to  school  five  days  each  week.  How 
many  days  do  you  stay  at  home? 

What  two  pieces  of  money  make  seven  cents? 

There  are  half  a  dozen  eggs  in  one  nest  and  one  in 
another.  How  many  eggs  in  both? 

Tell  a  story  about  7  —  1  =  6. 

Four  boys  and  three  girls  are  how  many  children? 

How  many  sides  have  a  triangle  and  a  square? 

Seven  boys  went  to  town,  but  only  five  returned.  How 
many  stayed  in  town? 

This  is  Tuesday.     How  many  more  days  in  this  week? 

There  were  seven  windows  in  a  room,  arid  two  of  them 
were  open.  How  many  were  shut? 

How  many  quarts  are  a  gallon  and  three  quarts? 


EIGHT  8. 


Eight 


8 


64.    How  many  dots  are  on  this  card? 

How  many  large  dots?     How  many  small  dots? 

Eight  dots  are  one  more  than  what? 

Here  are  six  blocks.     Give  me  enough  to  make  eight. 

Now  make  two  piles  of  them  with  the  same  number  in 
each.  How  many  blocks  in  each  pile? 

Take  one  block  from  one  pile  and  place  it  on  the  other. 
Now  how  many  in  each  pile? 

Take  one  block  from  the  smaller  pile  and  place  it  on 
the  larger.  Now  how  many  in  each  pile? 

Make  eight  dots  on  your  slate. 

Albert  may  erase  one  and  tell  how  many  are  left. 

Carrie  may  erase  two  and  tell  how  many  she  has  left. 

Jack  may  erase  three  and  tell  us  about  the  others. 

Jill  may  erase  four  and  tell  us  how  many  she  did  not 
rub  out. 

Count  to  eight,  then  back  to  one. 

Count  to  eight  by  twos.     How  many  twos  in  eight? 

Show  me  one  half  of  eight  blocks. 

How  many  fours  in  eight? 

Two  blocks  are  what  part  of  four  blocks? 


65.    Here  are  eight  stars. 


ft 


ft 


ft 


ft 


Into  how  many  parts  are  they  divided? 
*4 


50  SCHOOL    ARITHMETIC. 

Has  each  part  the  same  number  of  stars? 

One  of  the  four  equal  parts  of  anything  is  called 
one-fourth.  (Fourths  are  often  called  quartet's.) 

One  fourth  of  eight  stars  is  -      -  stars. 

Make  eight  tents.  Draw  a  ring  around  one  fourth  of 
them. 

Make  eight  dots.  Call  them  pigs.  Put  one  fourth  of 
them  into  a  pen. 

Now  put  another  fourth  of  them  into  a  pen. 

How  many  pigs  are  not  in  a  pen? 

What  part  of  the  eight  pigs  are  not  in  a  pen? 

How  many  fourths  of  the  eight  pigs  are  penned  up? 

Are  two  fourths  of  the  pigs  as  many  as  one  half  of  them? 

Ask  your  mamma  to  show  you  a  fourth  of  a  dollar,  and 
tell  me  all  you  can  about  it  to-morrow. 

One  fourth  (J)  of  eight  cents  is  -     -  cents. 

A  quart  is  what  part  of  a  gallon? 

Ask  your  papa  to-night  what  measures  are  used  to 
measure  potatoes,  and  tell  me  something  about  them 
to-morrow. 

Make  the  figure  that  stands  for  the  number  eight  — cf • 

66.    Copy,  complete  and  read: 

7  +  l  =  ();  5  +  3  =  ().  8-l  =  ().  8  — 4  =  (  ). 

6  +  2  =  ().  4  +  4  =  O-  8  — 2  =  ().  8-3  =  (). 

1  +  (  )  =  8.  3  +  (  )  =  8.  8  —  ()  =  l.  8  —  0  =  4. 

2  +  ()  =  8.  4  +  ()  =  8.  8-()  =  2.  8  —  0  =  3. 

Jof8  =  ().        i  of  4  =  O.        *  of  8  =  O. 


EIGHT  8.  51 

67.    How  many  pints  are  there  in  a  gallon  of  milk? 

If  you  drink  two  pints  of  it,  how  much  will  be  left? 

What  part  of  the  gallon  will  be  gone? 

Six  rats  were  caught  in  one  trap  and  two  in  another. 
How  many  rats  were  caught? 

Tell  a  story  about  5  +  3  =  8. 

Dick  has  four  marbles  and  John  has  four.  How  many 
have  they  both? 

How  many  fourths  of  this  square  .are  black  \ 

Is  one  half  of  the  square  white? 

One  square  is  what  part  of  four  squares? 

Two  squares  are  what  part  of  four  squares? 

Which  is  more — one  half  of  four  apples,  or  one  fourth 
of  them?  Draw  the  picture. 

One  half  of  anything  is  as  much  as fourths  of  it. 

Tell  a  story  about  8  —  5  =  3. 

A  boy  has  eight  rabbits.  Four  of  them  are  white.  The 
rest  are  black.  How  many  are  black? 

This  line  on  the  blackboard  is  two  yards  and  two  feet 
long.  What  is  its  length  in  feet? 

Ray  has  eight  cents  and  Elsie  has  a  nickel.  Ask  a 
question  and  answer  it. 


SCHOOL    ARITHMETIC. 


68.  Have  you  ever  seen  these  measures  2  Which 
measure  is  the  largest? 

Clyde  may  tell  me  some  of  the  things  he  has  seen 
measured  by  them.  Who  can  tell  me  something  more 
about  them? 

The  bushel  basket  is  full  of  corn.  Find  how  many 
times  you  can  fill  the  peck  measure  from  it. 

Find  how  many  times  you  can  fill  the  peck  measure  and 
empty  it  into  the  bushel  measure. 

In  one  bushel  there  are  -       -  pecks. 
4  pecks  make  1  bushel. 

When  you  buy  a  bushel  of  potatoes,  how  many  pecks 
do  you  get? 

A  peck  is  one  -     -  of  a  bushel. 

How  many  pecks  will  fill  the  half -bushel? 

If  a  bushel  basket  is  half-full  of  potatoes,  how  many 
more  pecks  of  potatoes  will  it  hold? 

Fill  the  peck  and  the  half-bushel  with  apples,  and 
empty  them  into  the  bushel  basket.  Is  the  basket  full? 
How  much  more  will  it  hold? 

How  many  half -bushels  does  it  take  to  fill  the  bushel? 

Two  pecks  are  what  part  of  a  bushel? 


NiNE  _  9.  53 

When  nuts  are  a  dollar  a  peck,  how  much  does  a  bushel 
cost? 

If  plums  are  worth  two  dollars  a  bushel,  how  much 
must  I  pay  for  a  half-bushel? 

There  are  eight  pecks  of  wheat  in  a  sack.  How  many 
bushels  are  in  it? 

If  we  eat  a  peck  of  apples  each  week,  how  long  will  a 
bushel  last? 

How  many  half-pecks  will  fill  the  bushel? 

A  peck  is  one  fourth  of  a  bushel. 

Two  pecks  are  fourths  of  a  bushel. 

Three  pecks  are  -      -  fourths  of  a  bushel. 

A  half:bushel  and  a  peck  are  -  -  pecks,  or  

fourths  of  a  bushel. 

Papa  bought  a  bushel  and  a  half  of  beets.  How  many 
pecks  did  he  get? 

How  much  must  you  pay  for  four  bushels  of  clover 
seed  at  two  dollars  a  bushel? 


Nine       •  •  •       9 


69.    How  many  more  than  eight  dots  are  on  this  card? 

Eight  dots  and  one  dot  are dots. 

There  are  three  dots  in  one  row.     How  many  in  two 
rows?   In  three? 

How  many  splints  are  needed  to  make  three  triangles? 
How  many  threes  in  nine? 


SCHOOL    ARITHMETIC. 

This  line  on  the  board  is  seven  inches  long,  and  this 
one  is  two  inches  long.  What  is  their  combined  length? 

Put  five  blocks  in  one  pile  and  four  in  another.  Put 
the  piles  together.  How  many  blocks? 

Take  three  blocks  away.     How  many  now  in  each  pile? 

Six  blocks  and  three  blocks  are  -      -  blocks. 

Make  nine  tents  with  splints.  Take  away  two.  How 
many  are  left? 

Cover  three  of  the  dots  on  the  card.  How  many  can 
you  see? 

Here  are  nine  beans.  Take  away  all  but  four.  How 
many  have  you  taken? 

Use  blocks  to  find  answers: 

Two  blocks  from  nine  blocks  leaves  —    -  blocks. 
Seven  blocks  from  nine  blocks  leaves  —     -  blocks. 
Three  blocks  from  nine  blocks  leaves  —     -  blocks. 
Six  blocks  from  nine  blocks  leaves  -      -  blocks. 
Four  blocks  from  nine  blocks  leaves  -     -  blocks. 
Five  blocks  from  nine  blocks  leaves blocks. 

Make  the  figure  that  stands  for  the  number  nine  —  ?. 
70.    Into  how  many  equal  parts  are  these  nine  dots 

divided?       |:.|:.|:. 

One  of  the  three  equal  parts  of  anything  is  called 
one,  third. 

One  third  of  nine  dots  is dots. 

One  third  of  six  stars  is  -      -  stars.     ^f  2/£  JA! 


NIKE  --  9. 

Into  what  is  this  circle  divided? 

What  part  of  it  is  black?  How  many  thirds  of  it  are 
white  ? 

One  third  of  the  circle  and  two  thirds  of  it  are  how 
much  of  the  circle? 

In  anything  there  are  -      -  thirds. 

Make  9  dots.  Draw  a  ring  around  one-third  (!)  of 
them. 

1          J-      ••*  £      ••* 

4-  of  •••    ==  -  .      %  of  •••    =  -  . 


Draw  a  line  3  of  9  inches  long. 
Draw  a  line  f  of  9  inches  long. 
Show  me  t  of  six  splints. 
Show  me  %  of  six  splints. 
Show  me  J-  of  six  splints  (all  of  them). 
One  third  of  six  dollars  is  -  dollars. 
Two  thirds  of  six  dollars  is  -  dollars. 
Here  are  some  squares.    DDD     DDD     DDD 
Henry  may  make  3  squares  at  a  time  for  3  times. 
How  many  squares  has  he  made? 
How  many  squares,  then,  are  3  times  3  squares? 
How  many  are  3  times  3,  or  3  threes? 
How  many  times  is  3  squares  found  in  9  squares? 
Draw  a  line  9  inches  long.     Measure  it  with  a  3-inch 
measure. 

How  many  times  does  it  contain  the  3-inch  line? 


SCHOOL   ARITHMETIC. 


XXX 


D 

How  many  times  does  C  contain  A? 

C  is  how  many  times  A? 

How  many  times  does  I)  contain  B? 

D  is  how  many  times  B? 

B  is  what  part  of  D? 

A  is  what  part  of  C  ? 

D  is  how  many  times  A? 

A  is  what  part  of  D? 

C  is  what  part  of  D? 

71.     Copy,  complete  and  read: 

8  +  l==(.).  4  +  ()  =  9.  9-l  =  ().  9-4  =  (). 

7 +.2  —  (  ).  2  +  ()  =  9.  9  —  8  =  ().  9  — 6  =  (). 

6  +  3  =  (  ).  1  +  (  )  =  9.  9  -  2  =  (  ).  9  —  3  =  (  ). 

5  +  4  =  (  ).  3  +  (  )  =  9.  9  —  7  =  (  ).  9  —  (  )  =  4. 


3  times  •  •  •  = 
3  times  3         = 

00   =t° 


2  times  A  A  A  A 
2  times  4 

*«*(  ). 


2  times  D  D  D   = 

2  times  3 

A  A  A  =  *  of  (    ). 


NINE  __  9.  57 

72.    Make  a  story  for  8  +  1  =  9. 

Seven  days  and  two  days  are  how  many  days? 

There  are  six  eggs  in  a  dish.  If  I  put  in  three  more, 
how  many  will  be  there  ? 

Bertha  came  to  school  five  days  last  week  and  four  days 
this  week.  How  -many  days  did  she  come  ? 

Albert  had  nine  marbles  but  lost  two.  Ask  a  question 
and  answer  it. 

Ada  broke  three  of  her  nine  eggs.  How  many  had 
she  left? 

Homer  had  nine  dimes.  He  gave  six  dimes  for  a  book. 
How  much  had  he  left? 

Mamma  bought  nine  pairs  of  gloves,  and  gave  Susie 
four  pairs.  How  many  pairs  did  she  keep? 

Papa  had  nine  dollars;  he  spent  all  but  two  dollars  for 
shoes.  How  much  did  the  shoes  cost? 

Three  girls  wear  six  shoes.  How  many  does  one  girl 
wear? 

Mamma  took  nine  yards  of  cloth  to  make  three  dresses 
for  Bessie.  How  many  yards  in  each  dress? 

Frank  walked  nine  miles  in  three  days.  How  far  did 
he  walk  in  one  day? 

Tell  a  story  about  J  of  9  =  3. 


SCHOOL    ARITHMETIC. 


Zero 


73.    How  many  dots  do  you  see  on  this  card? 

If  your  two  hands  were  cut  off,  how  many  would  you 
have  left? 

Draw  a  line  four  inches  long  on  your  slate.  Rub  out 
four  inches  of  the  line.  How  much  of  it  is  left? 

Ida  had  two  pennies.  She  spent  them  for  a  pencil. 
How  many  pennies  had  she  left? 

Albert  had  four  apples.  He  ate  one  and  gave  three 
to  John.  Ask  a  question  and  answer  it. 

Make  a  picture  of  no  stars. 

Make  the  figure  that  stands  for  none  —  6>. 

The  figure  0  is  called  zero,  naught,  or  cipher. 
When  it  stands  alone  it  means  none  to  count;  but  we 
shall  soon  make  it  work  hard  in  a  "  double  team." 
Tell  a  story  about  5  —  5  =  0. 


Ten 


10 


74.    How  many  more  than  nine  dots  are  on  this  card? 
Nine  dots  and  one  dot  are  -      -  dots. 
How  many  fingers  and  thumbs  have  you? 
How  many  fives  do  you  see  on  the  card? 
Put  eight  pegs  in  one  pile  and  two  in  another.      ll<>\v 
many  pegs  in  both  piles? 


TEN  —  10.  59 

Put  one  peg  from  the  larger  pile  into  the  smaller.  Now 
how  many  in  each  pile?  In  both? 

Five  pegs  and  five  pegs  are  -      -  pegs. 

Lay  ten  blocks  in  a  row.  Take  one  away.  How  many 
are  left? 

Use  the  ten  blocks  to  find  these  answers: 

Two  blocks  from  ten  blocks  leaves  -  -  blocks. 
Eight  blocks  from  ten  blocks  leaves  —  -  blocks. 
Three  blocks  from  ten  blocks  leaves  -  -  blocks. 

Seven  blocks  from  ten  blocks  leaves blocks. 

Four  blocks  from  ten  blocks  leaves  -  -  blocks. 
Six  blocks  from  ten  blocks  leaves  -  —  blocks. 
Five  blocks  from  ten  blocks  leaves blocks. 

Make  ten  dots,  thus: 

How  many  times  did  you  make  five  dotGf 

Two  times  5  dots  are  dots. 

How  many  times  did  you  make  two  dots? 

Five  times  '2  dots  are  dots. 

Divide  ten  blocks  into  piles,  putting  2  blocks  in  each 
pile.  How  many  times  have  you  found  2  blocks  in  10 
blocks? 

Then  10  blocks  contains  2  blocks  -   —  times. 

10  blocks  divided  by  2  blocks  =  5. 

10  blocks  divided  by  5  blocks  =  2. 


60  SCHOOL    ARITHMETIC. 

Show  me  ten  splints.     Tie  them  in  a  bundle. 
How  many  splints  in   the  bundle?     How  'many  ones 
in  it?    How  many  tens? 


Ten  ones  ^nake  one  ten. 

One  ten  and  one  ten  are  -       -  tens. 

How  many  are  5  tens  and  5  tens? 

It  takes  more  than  one  figure  to  stand  for  the  number 
ten.  We  must  now  make  0  go  to  work.  Ten  is  written 
thus: 


Make  ten  dots.     Draw  a  ring  around  one-half  of  them. 
How  many  are  in  the  ring? 

75.  Copy  and  complete: 

8+2— (  ).       1+  9— (  ).  7+(  )=10.  10— 2=(  ). 

6+4— (  ).       4+()=10.  5+(  )=10.  10— 4=(  ). 

7+3=(  ).       6+()= 10.  2+(  )=10.  10— 6— (  ). 

5+5=(  ).       3+(  )=1Q.  8+(  )=10.  10— 3— (  ). 

10— 5— (  ).  10— ()=  7.  10— (  )=  8.  J  of  10— (  ). 

76.  Write  with  proper  signs: 

From  10  take  3;     5;     7;     6;  8;     4. 

From  9  take  4;     3;     6;     8;  5;     7. 

To  3  add  4;     6;     5;     7;     2;  3. 

To  2  add  5;     8;     7;     6;     4;  0. 

Find  one-half  of  10;     8;     D;  4;     1. 

Find  one-third  of  9;     6;     3;  1. 
Find  one-fourth  of  8;     4;     1. 


TEN  -  10.  61 

77.    Dan  walked  8  miles  on  Monday  and  2  miles  on 
Tuesday.    How  far  did  he  walk  in  both  days? 

Tell  a  story  about  10  —  2  =  8. 

The  white  hen  has  seven  chicks  and  the  black  hen  has 
3.    How  many  have  they  both? 

Give  a  story  for  10  —  3  =  7. 

George  worked  6  days  last  week  arid  4  days  this  week. 
How  many  days  did  he  work? 

Sadie  bought  10  yards  of  gingham.     She  used  4  yards 
for  aprons,  and  had  -  --  yards  left. 

How  many  nickels  are  worth  10  cents? 

If  you  wish  to  pay  me  10  cents,  how  many  times  must 
you  give  me  5  cents? 

Two  times  5  cents  =          -  cents. 

How  many  5-cents  in  10  cents? 

If  I  give  you  2  cents  five  times,  how  much  money  will 
you  have? 

Five  times  2  cents  =='-       -  cents. 

ooo      ooo      ooo      ooo 


If  one  hat  costs   3  dollars,  three  hats  will  cost  - 
dollars. 

How  much  wyill  five  2-cent  stamps  cost? 

For  9  cents  I  can  buy  -      -  2-cent  stamps,  and  I  shall 
have  -  #  left. 

How  many  2-cents  in  10  cents  ?   (Make  the  picture.) 
divided  by  2^  means,  how  many  2$  are  there  in 


SCHOOL    ARITHMETIC. 


How  often  can  you  cut  2  yards  of  silk  from  a  piece  10 
yards  long?     10  yd.  divided  by  2  yd.  =  (  ).      - 

Mamie  went  to  the  store  with  10  cents  in  her  pocket. 
She  spent  one-half  of  it.     How  much  money  had  she  left? 


Tens. 


78.    How  many  cents  equal  a  dime? 

Then  how  many  ten-cents  is  a  dime  worth? 

How  many    ten-cents    are    the    dimes  on  the  left-hand 
card  worth?     On  the  right-hand  card? 

Two  ten-cents  and  three  ten-cents  are  -       -  ten-cents. 

Eight  dimes  and  two  dimes  are  -     -  dimes. 

Two  dimes  are  worth  twenty  cents. 

Place  ten  blocks  in  a  column  as  in  the  picture. 

Make  another  column  of  ten  blocks.      How 
many  blocks  in  both  columns? 

10  blocks  and  10  blocks  are  -       -  blocks. 

One  ten  and  one  ten  are  -       -  tens,  or  twenty.     We 
write  twenty  thus  —  -^^. 

Make  another  column  of  ten  blocks.     How  many  tens 
have  you  now? 

2  tens  and  1  ten  are  -      -  tens,  or  thirty. 
20  blocks  and  10  blocks  are  blocks. 


Twenty  means  two  tens;  what  does  thirty  mean? 


TENS. 


63 


In  20  the  figure  2  stands  for  two  tens,  the  0  for  no  ones. 
Now  who  can  write  thirty,  or  three  tens  and  no  ones? 
Let  me  see  who  can  write  forty,  or  four  tens  and  no 
ones? 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10  1     =   one  ten. 

• 

=   one  ten. 

=   one  ten. 

3  tens  =  30. 

79.  Supply  the  figures  needed: 

One  ten  and  no  one  is  written  thus  —  10.  Ten. 

Two  tens  and  no  ones  is  written  thus  —  20.      Twenty. 
Three  tens  and  no  ones  is  written  -thus  —  30.  Thirty. 
Four  tens  and  no  ones  is  written  thus  —  Forty. 

Five  tens  and  no  ones  is  written  thus  —  Fifty. 

Six  tens  and  no  ones  is  written  thus  —  Sixty. 

Seven  tens  and  no  ones  is  written  thus  —  Seventy. 

Eight  tens  and  no  ones  is  written  thus  —  Eighty. 

Nine  tens  and  no  ones  is  written  thus  —  Ninety. 

Ten  tens  and  no  ones  is  written  thus  —  100.  One  hundred. 

Sixty    means    six    tens.      What    does    seventy    mean? 
Eighty?    Ninety? 

80.  Count  by  tens  to  one  hundred. 
How  many  tens  make  100? 

How  many  cents  in  a  dollar?    How  many  dimes? 
How  many  tens  make  fifty? 


64  SCHOOL    ARITHMETIC. 

How  many  dimes  are  worth  50  cents? 
Six  ten-cent  pieces  are  worth  -      -  cents. 
Four  dimes  and  three  dimes  are  -      -  dimes,  or  - 
cents. 

Five  tens  and  four  tens  are  --  tens,  or  -    —  . 

Ten  tens  less  two  tens  are  -  —  tens,  or  -    —  . 

Three  tens  from  eight  tens  leaves  -      -  tens,  or  -    —  . 

One-half  of  6  tens  is  -      -  tens,  or  -    —  . 

We  gave  2  ten-dollar  bills  for  our  cow.  How  many 
dollars  was  that?  (Twenty  dollars  is  written  thus  —  $20.) 

This  book  is  worth  4  dimes,  or  -     -  cents. 

Dora  had  10  dimes.  She  spent  4  of  them,  and  had 
left  -  dimes,  or  -  cents. 

20  No  ones  and  no  ones  are  how  many  ones  ?  2  tens  and  3  tens 
30  are  how  many  tens  ?  Then  20  +  30  =  5  tens  and  no  ones,  or  50. 
50 

81.     Add: 

2  dimes  20^  4  dimes 

3  dimes  30^  4  dimes 

5  dimes  50^  2  dimes  20^ 

1  dime  10^  5  dimes 


3  dimes  30^  3  dimes 

3  dimes  30^  4  dimes 


4  tens  40  5  tens  50 

2  tens  20  3  tens  30 


TENS. 


65 


30  days 

30  days 

70  bushels 

30  bushels 


10  ft. 
60  ft. 

$50 

$50 


$40 
$50 

70  yd. 
20  yd. 


$60 

$40 

20 
60 


82.    Subtract 

4  dimes 
1  dime 


40^ 


7  dimes 
1  dime 


6  dimes 
3  dimes 


7  dimes 
2  dimes 


20^ 


8  tens 
4  tens 

$60 

$20 


80 
40 

80  ft. 
20  ft. 


10  tens 
5  tens 

90  pecks 
80  pecks 


100 
50 

$100 
$  10 


83.    Copy  and  complete: 


10  +  10  =  (  ). 

20  +  20  —  (  ). 

50  +  30  —  (  ). 

20  +  10  =  (  ). 

30  +  20  =  (  ). 

60  +  30  —  (  ). 

30  +  10-  (  ). 

40  +  20  —  (  ). 

70  +  30  —  (  ). 

40  +  10  —  (  ). 

50  +  20  —  (  ). 

40  +  40  —  (  ). 

50  +  10  =  (  ). 

60  +  20  —  (  ). 

50  +  40  —  (  ). 

60  +  10  =  (  )• 

70  +  20  —  (  ). 

60  +  40  —  (  ). 

70  +  10  —  (  ). 

80  +  20  —  (  ). 

50  +  50  =  (  ). 

80  +  10  =  (  ). 

30  +  30  —  (  ). 

20  +  10  —  (  ). 

90  +  10  —  (), 

40  +  30  —  (  ). 

30  +  10  =  (  ). 

66 


SCHOOL    ARITHMETIC. 


Review  and  Drill. 
84.    Copy  and  add: 


$3 

4  gal.            3 

ft.            1  ten 

10 

$1 

2  gal.           4 

ft.            2  tens 

20 

2  gal. 

3  in.              4^ 

'               4  tens 

40 

3  gal. 

2  in.              2< 

5               3  tens 

30 

$7 

6  doz.            5 

in.            8  tens 

80 

$1 

1  doz.           4 

in.           2  tens 

20 

85.    Copy 

and  subtract: 

7  ft. 

6  doz.            5^ 

*                6  tens 

60 

3  ft. 

4  doz.           2^ 

•                2  tens 

20 

$8 

7  in.             8 

gal.         5  tens 

50 

$5 

4  in.              6 

gal.         3  tens 

30 

9  yd. 

$9                  10  qt.         10  tens 

100 

6  yd. 

$4                   7 

qt.            8  tens 

80 

86.    Copy 

and  complete: 

3+2—  (  ). 

3+4—  (  ). 

3+6=(  ). 

6—  2=( 

4+1—  (  ). 

7+1—  (  ). 

5+4=(  ). 

5—  3=^=( 

l+5=(  ). 

2+6—  (  ). 

9+1—  (  ). 

7-5-( 

2+4—  (  ). 

5+3—  (  ). 

2+8—  (  ). 

6—  4—  ( 

3+3—  (  ). 

4+4—  (  ). 

7+3—  (  ). 

8—  5—  ( 

6+1—  (  ). 

1+8—  (  ). 

4+6—  (  ). 

7—  3=( 

2+5=(  ). 

7+2—  (  ), 

5+5=(  ), 

8—  6=( 

REVIEW    AND    DRILL.  67 


5+(  )=8. 

8—  3=(  ). 

10—  2=(  ). 

10-(  )=7. 

7+(  )=9. 

9—  2=(  ). 

10—  7=(  ), 

10—  (  )=2. 

3+(  )=7. 

7—  4=(  ). 

10—  4=(  ). 

10-(  )=6. 

4+(  )=8. 

8—  3=(  ). 

10—  5=(  ). 

10—  (  )=4. 

6+(  >=9. 

9—  7=(  ). 

10—  6=(  ). 

10—  (  )=8. 

2+(  )=7. 

7-5=(  ). 

10—  8=(  ). 

10_(  )=l. 

8=2+(  ). 

7=2+(  ). 

3=7—  (  ). 

i  of    4=(  ). 

6=4+(  ). 

9=5+(  ). 

2=5—  (  ). 

i  of    8=(  ). 

9=6+(-  ). 

6=4+(  ). 

1=8—  (  ). 

i  of    8=(  ). 

7=3+(  ). 

8=3+(  ). 

3=6—  (  ). 

i  of    6=(  ). 

9=7+(  ). 

10=6+(  ). 

4=9—  (  ). 

Jof  10=(  ). 

8=5+(  ). 

10=3+(  ). 

6=9—  (  ). 

i  of    9=(  ). 

87.    Add  quickly: 


4 

2 

1 

3 

4 

2 

6 

4 

3 

2 

3 

4 

3 

3 

5 

1 

4 

5 

6 

1 

2 

1 

3 

7 

4 

1 

2 

2 

7 

7 

8 

6 

2 

5 

9 

8 

88.    Subtract  quickly: 


3 

4 

5 

5 

6 

6 

6 

6 

7 

1 

2 

2 

3 

2 

4 

3 

5 

1 

7 

7 

7 

7 

7 

8 

8 

8 

8 

6 

2 

5 

3 

4 

4 

2 

3 

5 

8 

8 

9 

9 

9 

9 

10 

10 

10 

6 

7 

2 

7 

3 

4 

4 

6 

7 

68 


SCHOOL    ARITHMETIC. 


89.    Add  the  number  in  the  center  to  each  of  the  other 
numbers  in  the  same  square.     Name  results  at  sight: 


9 

7 

4 

6 

1 

8 

3 

5 

2 

8 

4 

5 

1 

2 

3 

6 

2 

7 

5 

4 

7 

1 

3 

2 

6 

0 

3 

90.  Subtract  the  number  in  the  center  from  each  of 
the  other  numbers  in  the  same  square.  Name  results 
quickly : 


7 

4 

3 

5 

2 

10 

9 

8 

6 

6 

8 

4 

10 

3 

7 

5 

3 

9 

5 

6 

8 

9 

4 

9 

4 

10 

7 

n     n 
n 
n     n 

n 

n  n 

Q  0 
Q  Q 

Q 

Q 

91.  Rob  made  5  squares  and  Roy  made  3.  How  many 
did  both  make?  Draw  the  picture. 

Dick  had  six  marbles.  He  gave  2  to  Ned.  How  many 
had  he  left?  Draw  the  picture. 

There  are  5  boys  and  4  girls  in  a  class.  How  many 
children  ? 

May  had  7  apples.  She  ate  2.  How  many  had  she  left? 
Draw  the  picture. 


WRITING  AND  BEADING  NUMBERS  TO  100.  69 

How  many  feet  are  there  in  3  yards? 

How  many  2-dollar  bills  should  I  get  for  a  10-dollar  bill? 

A  man  had  ten  sick  sheep.  One-half  of  them  died. 
How  many  got  well  ? 

A  lady  sold  8  pounds  of  butter,  2  pounds  in  a  roll.  How 
many  rolls? 

It  is  2  miles  from  Harry's  home  to  school.  How  far 
does  Harry  walk  each  day?  How  far  in  two  days? 

Two  wagons  and  a  bicycle  have  how  many  wheels? 

A  farmer  has  9  acres  of  wheat.  One-third  of  it  is  cut. 
How  much  has  he  to  cut  yet?  How  many  thirds? 

Bert  has  a  dime.    How  can  he  give  me  J  of  it? 

At  two  cents  each,  what  will  5  oranges  cost? 

If  $4  is  J  of  my  money,  how  much  have  I? 

Two  years  is  i  of  John's  age.    How  old  is  he? 

Writing  and  Reading  Numbers  from  1  to  100. 


:       : 


•  • 


11  12  13  14  15 

Eleven      Twelve      Thirteen      Fourteen      Fifteen 

92.  Look  at  the  number  picture  on  the  left.  What 
do  you  see  over  the  1  at  the  right  in  this  picture?  (1  one.) 

Over  the  one  at  the  left?  (1  ten.)  Then  It  means  1  len 
and  1  one.  (The  figures  11  stand  for  the  number  eleven.) 

What  do  you  see  over  the  2  in  the  second  number  pic- 
ture? (2  ones.)  Over  the  1?  Then  12  means  1  ten  and 
2  ones.  (The  figures  12  stand  for  the  number  twelve.) 


70 


SCHOOL    ARITHMETIC. 


What  does  13  mean?    17?     18? 

How  would  you  write  one  ten  and  three  ones  (thirteen)  ? 
One  ten  and  four  ones  (fourteen)  ?  Qne  ten  and  five  ones 
(fifteen)? 

How  many  figures  do  you  write  for  each  number? 

What  does  the  figure  on  the  left  show? 

What  does  the  figure  on  the  right  show? 

In  which  place  do  we  write  the  ones  ?   The  tens  ? 

If  we  call  the  number  expressed  by  16,  sixteen,  what 
shall  we  call  the  number  expressed  by  17?  By  18?  By  19? 

93.    Read,  supplying  blanks: 

11  =    1  ten  and    1  one.  16  =  --  ten  and  --  ones. 

12  =  —  ten  and  —  ones. 

13  =  —  ten  and  —  ones. 


14  =    -  ten  and  —  ones. 

15  =  —  ten  and  —  ones. 


17  =  —  ten  and  —  ones. 

18  =  —  ten  and  —  ones. 

19  =  —  ten  and  —  ones. 

20  =    -  tens  (and  no  ones). 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

=    1  ten. 
=   1  ten. 
=   1  one. 

jj 

94.  You  have  already  learned  that  two  tens  and  no 
ones  is  written  thus  —  20. 

Try  to  write  two  tens  and  one  one. 

Now  write  two  tens  and  two  ones. 

What  do  we  call  2  tens? 

If  we  call  two  tens  and  one  one,  twenty-one,  what  shall 
we  call  two  tens  and  two  ones? 

What  shall  we  call  two  tens  and  three  ones?  Two  tens 
and  four  ones?  Two  tens  and  five  ones?  Two  tens  and 


WRITING  AND  READING  NUMBERS  TO  100. 


71 


six  ones?    Two  tens  and  seven  ones?    Two  tens  and  eight 
ones?    Two  tens  and  nine  ones? 
Copy  and  complete  this  table:* 


0 

10 

20 

30 

40 

50 

60 

70 

80 

90 

1 

11 

21 

31 

2 

12 

22 

3 

13 

4 

5 

6 

7 

8 

9 

95.   How  many  numbers  are  in  each  column? 
How  many  columns  are  there? 

Name  the  numbers  in  the  second  column,  beginning  at 
the  top. 

What  does  16  express?    (One  ten  and ones.) 

What  does  14  express?     18?     15? 

*  The  pupils  should  be  able  to  complete  this  table  without  help. 
When  they  have  it  finished,  they  should  learn  the  number  names — 
that  is,  count  to  one  hundred. 


SCHOOL    ARITHMETIC. 


Name  the  numbers  in  the  third  column. 

What  does  21  express?    23?    25?    29? 

What  do  we  call  3  tens  ?  Wliat  then  is  the  number  made 
up  of  3  tens  and  1  one?  (Thirty-one.) 

Now  name  the  numbers  in  the  fourth  column. 

What  does  31  express?     32?     36?    38? 

Name  the  numbers  in  the  fifth  column. 

What  does  41  express?    43?    44?    49? 

Name  the  numbers  in  each  of  the  other  columns. 

Count  to  one  hundred  without  looking  at  the  table. 

What  number  is  written  at  the  right  of  14?  At  the 
left  of  it? 

What  number  is  written  at  the  left  of  25?  At  the  right 
of  it? 

Begin  at  the  number  2  and  name  each  number  to  the 
right  of  it. 

Begin  with  6  and  read  across  to  96. 

Name  all  the  numbers  in  the  table  that  end  in  8.  In 
4.  In  7.  In  9. 


What  does 
ones? 


express?     Who  can  write  9  tens  and  10 


The  Sign  x. 
C  D 


E 


96.    How  many  squares  in  A?    B  is  how  many  times  A? 

A  is  2.     How  many  2's  in  B?     2  2's  are  -    — . 

2X2  =  4.    This  is  read,  2  2's  are  4,  or  2  times  2  are  4. 

(The  sign  X  stands  for  the  word  times.) 


THE    SIGN    X  •  73 

How  many  2's  in  C?     How  many  ones? 

Eead  this:  3X2  =  6. 

How  many  2's  in  D?  How  many  ones?  How  many 
fours  ? 

Complete  and  read:  4  X  2  =  (     ).     2  X  4  =»(     ). 

How  many  2's  in  E?  How  many  ones?  How  many 
fives? 

Complete  and  read:  5X2  =  (     ).     2  X  5  =  (     ). 


How  many  twos  on  the  card  to  the  left? 
How  many  threes  on  the  other  card? 
Are  3  2's  as  many  as  2  3's? 
Show  with  blocks  that  your  answer  is  correct. 
Read  these:  3X2  =  2X3.     3X2  or  2X3  =  6. 
Call  the  dots  on  the  first  card  cents.     How  many  of 
them  will  pay  for  a  2-cent  stamp? 

How  many  of  them  will  pay  for  3  stamps? 


97. 

1 

X2 

= 

2 

2 

X 

1  = 

2 

4 

» 

2 

X2 

= 

4 

2 

X 

2  = 

4 

I 

3 

X2 

= 

6 

or       2 

X 

3  = 

6 

• 
• 

.:: 

4 

4 

»       K 

X2 

V  9 

= 

8 
i  n 

2 

9 

X 

4  = 
K 

8 

How  i 

in 

my 

/\  ^ 

are 

2  i 

1  U 

2  4's? 

2 

3's? 

2  5 

<, 

2  1 

Copy  and  complete: 

2X()  =  4          2  X  (  )  =  2          2  X  (  )  =  10 
3X()  =  6         4X()  =  8          5X()  =  10 


SCHOOL    AKITHMETIC. 


98.  How  many  dots  on  the  card  at  the  left?  How 
many  3's? 

How  many  3's  do  you  see  on  the  second  card?  On  the 
third  card? 

Two  3's  are  how  many  ones?    2  X  3  =  (  ). 

Three  3's  are  how  many  ones?     3  X  3  =  (  ). 

Nine  dots  are  how  many  times  3  dots? 

Call  each  dot  on  the  middle  card  a  foot.  How  many 
of  them  are  a  yard  ?  How  many  yards  in  6  feet  ?  In  9  feet  ? 
3X2  — ().  2X()  =  6.  3X()  =  9. 

An  orange  costs  3  cents.  How  much  must  I  pay  for 
3  of  them? 

How  many  sides  have  three  triangles?     Three  squares? 

The  Sign  -T-. 


How  many  2-cent  stamps  can 
How  many 


99.    Here  are  6  cents. 
I  buy  with  them? 

How  many  2^  do  you  see  in  the 

How  often  must  2^  be  taken  to  make 

Then  6^  divided  by  2^  =  3  times.     This  may  be  writ- 
ten, 60-^-2^  =  3. 

It  means  that  2  cents  are  found  in  6  cents  3  times. 
6^  divided  by  3#  ==  (  ).     6^  -=-  3^  =  (  ). 

What  may  stand  for  the  words  divided  by? 


THE    SIGN 


Here  are  8  stars.          V,  ^°  ^ow  manv 


can  I  give  2  stars  each?    4  stars  each? 

8  stars  -f-  2  stars  =  (  ).     8  stars  -r-  4  stars  =  (  ). 

If  I  divide  the  stars  into  two  equal  parts,  how  many 
stars  will  be  in  each  group? 

Then  8  stars  -+-  2  =  4  stars.     8  stars  -r-  4  =  (  ). 

How  many  2's  in  4?    In  6?    In  8?    In  10? 

How  many  3's  in  6  ?    How  many  in  9  ? 

How  many  4's  in  8?    How  many  5's  in  10? 

How  often  are  4^  contained  in  8^? 

Nine  quarts  contains  3  quarts  -      -  times. 

4-7-2  =  (  ).  6-f-2  =  (  ).  8-7-4  =  (  ). 

8 -5-2  ==(*).  6-^-3  =  (  ).          10-7-5  =  ( )• 

i  of  4  =  (  ).  J  of  6  =  (  ).  i  of  8  =  (  ). 


An  orange  costs  3^.    How  many  can  I  buy  for 

If  I  must  pay  5^  for  a  quart  of  milk,  how  many  quarts 
will  I  get  for  this  dime? 

Hettie  had  9  buttons,  3  in  a  row.  How  many  rows 
were  there? 

How  many  2-cent  tops  can  you  buy  for  8  cents? 

Cut  a  stick  9  inches  long  and  one  3  inches  long.  Com- 
pare them. 

The  longer  stick  is times  as  long  as  the  other. 

The  shorter  stick  is  — : —  as  long  as  the  other. 

How  many  times  can  a  2-inch  line  be  measured  off  on 
a  10-inch  line? 


76 


SCHOOL    ARITHMETIC. 


NUMBERS  TO  20. 
Eleven. 


• 
• 
• 

•• 
11. 


100.     Ten  dots  and  one  dot  are 
Eleven  is  made  up  of  1  ten  and 


dots. 


one. 


How  many  splints  are  in  the  bundle?  How  many  loose 
splints  are  there? 

What  figure  will  tell  the  number  of  bundles,  or  tens? 
The  number  of  single  splints,  or  ones  ? 

Take  11  pegs.  Place  them  in  two  piles,  putting  9  in 
one  pile. 

How  many  pegs  in  each  pile?    How  many  in  both? 

What  is  the  sum  of  9  pegs  and  2  pegs  ?    Of  9  and  2  ? 

Put  one  peg  from  the  larger  pile  on  the  smaller.  Xow 
how  many  in  each  pile? 

The  sum  of  8  pegs  and  3  pegs  is pegs. 

Take  another  peg  from  the  larger  pile  and  place  it  on 
the  smaller.  Now  tell  me  about  the  two  piles. 

Show  me  with  the  pegs  how  many  6  and  5  are. 

Take  one  peg  away  from  the  11.     How  many  are  left? 

Show  me  with  the  pegs  how  many  2  from  11  leaves. 
3  from  11.  4  from  11.  5  from  11.  6  from  11.  7 
from  11. 

Cut  a  string  a  foot  long.  Cut  off  1  inch  of  it.  Measure 
the  piece  that  is  left. 

Mary  may  tell  us  all  she  can  about  11. 


TWELVE. 


77 


101.  Copy  and  complete: 

10  +  1=         11  —  1=         11  —  6=      11  —  ()=    8 

3  +  8  =      11  —  4=        11  —  7  =        4  +  (  )  =  11 

7  +  4  =      11  —  3=        11  —  9=        11  —  (  )=    6 
5  +  6=      11  —  5=        11—10=       !!  —  ()=     4 

102.  Make  a  story  for  5  +  6. 

A  stick  of  candy  costs  a  cent.  How  many  sticks  can 
you  get  for  a  dime  and  a  cent? 

What  two  pieces  of  money  make  11  cents? 

How  much  must  you  pay  for  three  3-cent  stamps  and  a 
2-cent  stamp? 

If  you  have  been  at  school  two  weeks  and  one  day  this 
month,  how  many  days  have  you  been  at  school? 

Three  yards  and  two  feet  are  how^many  feet? 

We  have  2  bushels  and  3  pecks  of  apples.  How  many 
pecks  have  we? 

If  we  use  3  pecks  of  them,  how  many  pecks  will  we 
have  left?  How  many  busnels? 

A  rail  11  feet  long  was  cut  in  two.  One  part  was  7 
feet  long.  What  was  the  length  of  the  other  part? 

There  are  11  eggs  in  two  nests.  In  one  nest  there  are 
5  eggs.  How  many  in  the  other? 

Twelve. 


103.     Ten  dots  and  2  dots  are 
Twelve  dots  are  1  more  than 


-  dots, 
dots. 


78  SCHOOL    ARITHMETIC. 

There  are  12  dots  on  the  card  at  the  right.  Call  them 
pigs.  How  many  are  in  each  pen? 

Six  and  six,  or  two  sixes,  are  .  How  many  6's 

in  12? 

Put  one  little  pig  into  the  pen  with  the  big  ones.  How 
many  pigs  in  each  pen  now? 

Seven  and  five  are  how  many? 

Put  another  little  pig  in  with  the  big  ones.  Now  how 
many  pigs  in  each  pen? 

Eight  and  four  are  how  many? 

When  9  of  them  are  in  one  pen,  how  many  are  in 
the  other? 

When  only  two  little  pigs  remain  in  one  pen,  how  many 
are  in  the  other? 

Who  can  name  three  numbers  that  added  together 
make  12? 

Write  twelve  and  tell  what  each  figure  stands  for. 

Use  your  foot  rule  to  find  these  answers : 

One  inch  from  12  inches  leaves  -      -  inches. 
Two  inches  from  12  inches  leaves  -      -  inches. 
Four  inches  from  12  inches  leaves  -      -  inches. 

Eight  inches  from  1 2  inches  leaves inches. 

Three  inches  from  12  inches  leaves inches. 

Five  inches  from  12  inches  leaves  -  —  inches. 
Six  inches  from  12  inches  leaves  -  —  inches. 

How  many  triangles  can  you  make  with  12  splints? 
How  many  squares? 

Measure  your  rule  with  a  stick  2  inches  long.  How 
many  2-inches  make  12  inches? 

@  X  2  inches  = inches. 


TWELVE.  79 

How  many  times  could  you  cut  2  inches  off  your  rule? 
How  many  2's  in  12? 

12  inches  -f-  2  inches  =  -    — . 
Use  splints  to  show  me  J  of  12.     J  of  12.     f  of  12. 

104.     Measure  with  the  foot  rule: 

The.  length  of  this  book. 
The  width  of  your  desk. 
The  length  of  this  chart. 
The  height  of  this  boy. 
The  length  of  this  yardstick. 

Measure  with  the  yardstick: 

The  length  of  this  room. 
The  width  of  this  room. 
The  length  of  this  house. 

Your  foot  rule  is  marked  off  into  12  equal  parts.   What 
is  each  part  called? 

In  1  foot  there  are inches.     In  1  of  a  foot  there 

are inches. 

How  many  inches  in  -J  of  a  foot?    In  J  of  a  foot? 

Draw  a  line  on  the  board    12    inches    long,    without 
measuring. 

Now  measure  it  and  find  out  how  long  it  really  is. 

Who  can  draw  a  line  a  yard  long  without  measuring  it? 

Draw  a  rectangle  (an  oblong)  four    inches    long  and 
three  inches  wide. 

Draw  lines  across  it,  as  in  the  picture. 
Draw  them  an  inch  apart. 

What   is    a   square    1    inch    on    a   side 
called? 


80  SCHOOL    ARITHMETIC. 

How  many  square  inches  are  there  in  the  upper  row? 

How  many  rows  are  there?     Then  how  many  square 
inches  in  the  three  rows? 

3X4  square  inches  =  -  square  inches. 

How  many  square  inches  in  the  left-hand  row?     How 
many  rows  are  there? 

Then  how  many  square  inches  in  the  four  rows? 
4X3  square  inches  =  -     -  square  inches. 

Cut  out  a  square  inch  and  find  how  many  of  them  will 
cover  your  rectangle. 

Draw  a  rectangle  6  inches  long  and  2  inches  wide.   Find 
how  many  square  inches  there  are  in  it. 

105.      Copy  and  complete: 


10 

+  2  = 

12 

0  

12  —  () 

=  2 

9 

+    2 

11 

+  1  = 

12 

-4       

12  —  () 

-4 

7 

+    4 

9 

+  3  = 

12 

-4  = 

12  —  (  ) 

=  3 

i 

4 

of  12 

4 

+     0 
O  — 

12 

-3  = 

12—  (  ) 

=r  5 

i 

of  12 

7 

+  5  = 

12 

-5  = 

12-(  ) 

=  7 

i 

of  12 

6 

+  6  = 

12 

/>  

12  —  () 

1  =  8 

^ 

of    9 

2 

X  6  = 

12 

-4-2  = 

12  -^  3 

= 

i 

of  12 

3 

X4  = 

12 

-5-6  = 

12  -T-  4 

= 

1 

of  12 

106.  There  are  9  quarts  of  milk  in  one  pail  and  3 
quarts  in  another.  How  much  milk? 

Tell  a  story  about  8  +  4  =  12. 

How  many  days  are  a  week  and  5  days? 

Seven  cents  and  a  nickel  are  how  much  money? 

Henry  had  12  goats.  A  bad  boy  stole  4  of  them.  Ask 
a  question  and  answer  it. 

Make  a  story  about  12  —  5  =  7. 


TWELVE.  81 

A  boy  who  had  12  cents  gave  two  nickels  for  a  book. 
He  had  left cents. 

How  many  cows  have  12  tails?  How  many  have  12 
horns  ? 

Six  girls  wear  —  -  shoes. 

How  many  shoes  do  3  horses  wear? 

In  1  yard  there  are  feet.  In  4  yards  there  are 

feet. 

Twelve  pecks  of  plums  are  how  many  bushels? 

A  log  is  12  feet  long.     How  many  yards  is  that? 

If  you  divide  12  nuts  equally  among  4  boys,  how  many 
will  each  have? 

How  many  quarts  of  milk  in  12  pints? 

If  we  had  a  dozen  eggs, boys  could  have  2  apiece. 

107.     Name  the  months  of  the  year. 

In  a  year  there  are months.  In  half  a  year  there 

are  -  -  months. 

What  is  the  first  month?     The  second?     The  twelfth? 

What  is  the  name  of  the  present  month?  In  what 
month  is  your  birthday? 

During  what  months  is  school  held? 

March,  April,  and  May  are  called  the  spring  months. 
Name  the  summer  months.  The  fall  or  autumn  months. 
The  winter  months. 

How  many  seasons  in  a  year?  Then  how  many  months 
in  a  season? 

What  part  of  a  year  are  the  spring  months?  The 
summer  months? 

What  part  of  a  year  are  the  spring  and  summer  months 
together  ? 


82 


SCHOOL    ARITHMETIC. 


108.      Some  things  to  remember: 

Jan.    stands  for  January.  Sept.  stands  for  September. 

Feb.    stands  for  February.  Oct.    stands  for  October. 

Mar.    stands  for  March.  Nov.  stands  for  November. 

Aug.  stands  for  August.  Dec.  stands  for  December. 


12  inches    make  1  foot. 
12  things    make  1  dozen. 
12  months  make  1  year. 

Ct.  or  $  stands  for  cent. 
Qt.  stands  for  quart. 
Gal.  stands  for  gallon. 


In.  stands  for  inch  or  inches. 
Ft.   stands  for  foot  or  feet. 
Doz.  stands  for  dozen. 

Sq.  in.  stands  for  square  inch. 
Yd.  stands  for  yard. 
Bu.  stands  for  bushel. 


109.  It  is  noon  at  12  o'clock.  Look 
at  the  'clock  face  and  tell  how  many 
hours  it  is  from  noon  to  midnight. 

Show  me  to  what  the  short  hand 
points  at  1  o'clock.  At  2  o'clock. 

What  stands  for  one  on  the  clock 
face?  For  two?  For  three?  For 
fivel  For  ten\ 


I  stands  for  1. 

II  stands  for  2. 

Ill  stands  for  3. 


V  stands  for 
X  stands  for 
What  stands 


5. 
10. 
for  4? 


In  Roman  notation  IV  always  stands  for  4  except  on 
clock  faces,  where  IIII  is  commonly  used. 

You  know  that  5  —  1  means  4,  or  1  less  than  5.  When 
I  is  written  before  V,  the  two  letters  (IV)  mean  one  less 
than  five,  or  4. 


THIRTEEN. 


83 


What  do  you  think  IX  means? 
What  does  5  +  1  mean? 

When  I  is  written  after  V,  the  two  letters  (VI)  mean 
one  more  than  five,  or  6. 

What  do  you  think  VII  means?     VIII?     XI?     XII? 

IV  stands  for  4.  X  stands  for  10. 

VI  stands  for  6.  IX  stands  for     9. 

VII  stands  for  7.  XI  stands  for  11. 

VIII  stands  for  8.  XII  stands  for  12. 

If  we  eat  dinner  at  12  o'clock  and  supper  at  6  o'clock, 
how  long  is  it  between  meals? 

Look  at  a  nickel  to-night  and  tell  me  to-morrow  what 
shows  the  number  of  cents  it  is  worth. 


Thirteen. 


110.      What  number  follows  12? 

One  ten  and  3  ones  are . 

Name  two  numbers  less  than  10  whose  sum  is  13.  Two 
other  numbers.  Now  two  others.  (Use  splints  to  find 
the  numbers.) 

Take  13  splints.  Show  how  many  are  left  when  4  are 
taken  away.  When  5  are  taken  away.  When  6  are  taken 
away. 

This  line  on  the  board  is  13  inches  long.  How  much 
longer  is  it  than  your  foot  rule? 

How  many  splints  are  in  the  bundle?    How  many  tens? 

How  many  loose  splints,  or  ones,  do  you  see? 


84 


SCHOOL    ARITHMETIC. 


Write  on  the  board  the  figures  that  stand  for  the 
number  thirteen. 

Which  figure  stands  for  the  tens?    Which  for  the  ones? 

Three  and  ten  are  -  .  (The  word  thirteen  means 
three  and  ten.) 

111.     Copy  and  complete: 

10  +  3=  13  —  4-  11  +  2=  8  +  2  +  3  = 

9  +  4=  13  —  6=  13  —  (  )  =  9  5  +  4  +  4  = 

5  +  8=  13  —  7=  13  —  (  )  =  7  4  +  3  +  6  = 

7  +  6=  13  —  5=  13  —  ()  =  5  5  +  3  +  5  = 


112.    Add  quickly: 


532 
8     10     11 


Subtract  at  sight: 

13     13     13     13     13     13     13     12     12     12 

465789     10       354 


Subtract  each  number  in  the  rim  of  the 
wheel  from  the  13  in  the  center. 

113.      Three  bushels  and  a  peck  are  how 
many  pecks? 

There  are  8  qt.  of  milk  in  one  pail  and  5  qt.  in  another. 
How  much  milk  111  both  ? 


FOUKTKKX. 


85 


Look  at  the  flag  and  tell  a 
story  about  7  -|-  6. 

How  many  4's  in  13,  and 
how  many  left  over  ?  Draw  the 
picture,  using  dots. 

A  log  is  4  yd.  and  1  ft.  long. 

It  is feet  longer  than  a  pole 

ten  feet  long. 

Fourteen 


114.      One  ten  and  4  ones  are 


How  many  squares  do  you  see  in  the  figure? 

How    many  more    than    10?     How  many  more 
than  9?     Than  8?    Than  7? 

If  5  were  taken  away,  how  many  would  be  left? 

Take  six  away  from  14.     How  many  remain? 

Count  by  twos  to  14.     !!!!!!! 

How  many  dots  are  in  each  row?     How  many 
rows  ? 

Two  times  7  dots  are dots. 

Show  that  7  times  2  dots  are  as  many  as  2  X  7  dots. 

One-half  of  14  dots  is  — dots. 

How  many  7's  make  14?     How  many  2's? 

Take  9  splints  and  5  splints  and  show  that  they  are  as 
many  as  one  ten  and  four  ones. 

Write  the  figures  that  stand  for  the  number  fourteen. 

Which  figure  stands  for  the  ones?     On  which  side  of 
the  1  must  it  stand? 


86  SCHOOL    ARITHMETIC. 

115.  Copy  and  complete: 

9  +  5=  14—6=  5  +  (  )  =  14  2X7  = 

6  +  8=  14  —  7  =  8  +  (  )  ==  14  7X2-= 

7  +  7=  14  —  8=  14  —  ()=      9  14 -f- 2  = 
14  —  5=  14— ,9=  14  — ()=      6  14  -v- 7  = 

2  qt.  +  1  pt.   =  -      -  pt.  3  ga..  +  2  qi.   =  -      -  qt. 
7  bu.  +  3  bu.  =  -                       $10      +  $4       = 

1  ft.    +2  in.   =  -      -  in.  5  qt.     +  3  pt.  = pt. 

3  yd.  -4-  5  ft.    = ft.  i  doz.  +  5 

116.  James  earned  8  cents  on  Friday  and  6  cents  on 
Saturday.     On  both  days  he  earned  -     -  cents. 

How  much  will  6  eggs  cost  at  14  cents  a  dozen? 

In  14  there  are 3?s  and  —    -  over. 

Make  a  story  for  7  +  7  =  14. 

How  many  days  are  there  in  two  weeks? 

How  many  gloves  are  7  pairs  of  gloves? 

Fourteen  months  are  how  many  more  months  than  a 
year  ? 

A  boy  had  a  ten-cent  piece  and  four  pennies.  He  spent 
5  cents  for  peanuts.  How  much  had  he  left? 

A  spider  has  8  legs.  A  spider  and  a  fly  together  have 
14  legs.  How  many  legs  has  a  fly? 

Three  gallons  and  2  quarts  of  milk  are  how  many  quarts? 

How  many  half -bushels  of  oats  make  7  bushels  ? 

If  a  milkman  has  7  qt.  of  milk,  to  how  many  persons 
can  he  sell  a  pint  each? 

A  man  has  14  miles  to  travel.  When  he  has  gone  8 
miles,  how  far  has  he  yet  to  go? 


FIFTEEN. 

Fifteen. 


87 


117.    One  ten  and  5  ones,  or  one  ten  and  1  five,  are  -    — . 

Lay  10  blocks  in  one  row  and  5  in  another,  as  in  the 
picture  above.  Use  them  to  find  the  missing  number  in 
the  following: 

15=9+(  ).  l5=8+().  15=6+(  ).  15=7+(  ). 
15— 6=(  ).  15—  8=( J').  15— 7=(  ).  15— 9=(  ). 
15=3  X(  ).  15=5X(  ).  15-HJ==<  ).  15-^3=(  ). 

How  many  dots  are  on  the  card?     What  part  of  them 
are  on  the  right  of  the  line?     On  the  left  of  the  line? 
Are  3  fives  as  many  as  5  threes?     Show  with  counters. 


118.      This    circle    is    divided    into 


equal    parts. 


What  do  you  think  one  of  these  parts  is  called? 
What  part  of  the  rectangle  is  dark? 
One  of  the  5  equal  parts  of  anything  is  called  one-fifth 


To    find    one-fifth    of 
into  -     -  equal  parts. 


anything    we    must    divide  it 


How  many  small  squares  are  there  in  the  rectangle? 
Are  the  3  dark  squares  one  of  the  5  equal  parts  of  the 
rectangle? 


88  SCHOOL    ARITHMETIC. 

Then  J  of  15  squares  is  -     -  squares. 

One-fifth  of  5  cents  is  -     -  cent. 

One-fifth  of  10  feet  is  -     -  feet. 

Make  15  dots.  Draw  a  line  around  i  of  them.  Now 
draw  a  line  around  another  fifth  of  them. 

How  many  fifths  have  lines  around  them?  How  many 
fifths  have  no  lines  around  them? 

How  many  dots  in  one  fifth?    How  many  in  two  fifths? 

Then  f  of  15  dots  =        -  dots. 

119.      Copy  and  complete: 


9+6= 

15—6= 

7+(  )=15. 

3X5: 

7+8= 

15—7= 

9+(  )=15. 

5X3 

1  of  15= 

15—9= 

15—  (  )=10. 

15-^5= 

I  of  15= 

15—8= 

15-(  )=  6. 

15-=-3: 

i  of  15= 

J  of  15= 

f  of  15= 

t  of  15 

120.  A  man  has  3  five-dollar  bills.  How  much  money 
has  he? 

What  two  pieces  of  paper  money  make  $15?  What  3 
pieces  ? 

Fifteen  eggs  are  how  many  more  than  a  dozen? 

Tell  a  story  about  9  boys  +  6  girls  =  15  children. 

Punch  has  8  dimes  and  Judy  7.  Ask  a  question  and 
answer  it. 

Jennie  has  5  yd.  of  cloth  for  a  dress.  How  many  feet 
long  is  the  cloth? 

Tell  a  story  about  15  —  6  ==  9. 

Stella  had  15  jacks.  She  lost  7  of  them.  She  had 

left. 

Harry  may  tell  all  he  can  about  15. 

Find  out  at  home  to-night  how  many  ounces  make  a 
pound. 


SIXTEEN. 

Sixteen. 


89 


121.      One  ten  and  six  ones  are  -  —  . 
Show  with  blocks  how  many  9  and  7  are. 
How  many  ones  do  you  see  on  the  card?     How  many 
8's?     How  many  4's?     How  many  2's? 
Show  with  blocks  how  many  16  —  7  are. 
How  many  times  4  dots  make  16  dots? 
How  often  does  the  card  contain  8  dots? 
If  the  dots  were  shoes,  how  many  pairs  could  you  take? 
If  they  were  quarts,  how  many  gallons  would  you  have? 
What  part  of  the  dots  is  on  each  side  of  the  line? 
What  part  of  the  16  dots  are  large? 
How  many  fourths  of  them  are  small? 
Sixteen  means  six  and  —  •—  . 


122.      Copy  and  complete: 

+  7=  iof!6= 


8  +  8= 
10  +  6= 


|-  of  16= 
of  16- 


2X8 
8X2 
4X4 


16-^-8 
16-^-2 

16  ~-  4 


123.  Tom  had  9  cents  and  Sam  had  7  cents.  They 
both  had  --  cents. 

They  gave  ten  cents  of  it  for  a  dime.  How  many 
pennies  had  they  left? 

Cora  carried  2  gallons  of  water  and  Delia  carried"  8 
quarts.  How  much  did  both  carry? 

We  have  4  cows.  Each  cow  gives  4  quarts  of  milk. 
They  all  give  -  quarts. 


90 


SCHOOL    ARITHMETIC. 


Mr.  Brown  had  16  sheep,  but  one-half  of  them  died. 
Ask  a  question  and  answer  it. 

How  many  wheels  have  8  bicycles? 

I  have  16  apples.  To  how  many  girls  can  I  give  two 
apples  each  ? 


124.   Where  have  you  seen  these  weights  used? 
Which  is  the  largest  weight?    The  smallest? 
How  many  of  the  smallest  are  equal  to  the  largest? 
How  many  ounces  make  a  pound? 

16  ounces  (oz.)  make  1  pound  (lb.)« 

What  stands  for  the  word  ounce  or  ounces?  For  the 
word  pound  or  pounds? 

How  many  ounces  in  ^  of  a  pound?     In  J  of  a  pound? 

What  part  of  a  pound  are  8  ounces?     4  ounces? 

How  many  ounces  in  a  quarter  of  a  pound  of  starch? 

How  many  4-ounce  weights  are  equal  to  the  1 -pound 
weight?  How  many  2-ounce  weights? 

When  butter  is  16  cents  a  pound,  how  much  must  I 
pay  for  8  ounces?  For  4  ounces?  For  12  ounces,  or  f 
of  a  pound? 

Seventeen. 


125,      Ten  and  seven  are  how  many?    How  many  more 
would  make  2  tens? 

What  does  the  word  seventeen  mean? 


SEVENTEEN. 


91 


How  many  dots  are  on  the  card?  How  many  on  each 
end  of  it? 

Nine  dots  and  eight  dots  are dots. 

If  8  dots  were  taken  off  the  card,  how  many  would 
remain?  How  many  if  9  dots  were  removed? 

Count  12  by  twos.  What  other  numbers  can  you  count 
by  twos?  Can  you  count  9  by  twos? 

Numbers  that  can  be  counted  by  twos  are  called  even 
numbers;  all  others  are  called  odd  numbers. 

Did  you  ever  play  "  Odd  or  Even" ?  How  do  you  play  it? 

Is  5  odd  or  even  f 

Name  all  the  odd  numbers  less  than  17. 


Tell  at  sight  what  number  put  with 
each  of  the  outer  numbers  will  make  17. 


126.     Add: 
9       10 

8         7 


10 

8 

14 

12 

17 

7 

15 

11 

9 

11 

6 


5 
12 


13 
4 


3 
14 


15 

2 


Subtract: 
17       17 
8       10 


17 
9 


16 


16 

9 


16 
6 


16 

7 


15 

6 


127,      Is  9  odd  or  even?    How  many  2's  in  9? 


y  - 

>j 

—  2  — 



-  ana   - 

-   leit   over. 

i 

1  ^ 

• 

J.O 

14. 



17 

A  

-L  t 
17 

T 
ft  

92  SCHOOL    ARITHMETIC. 

128.     Nine  cents  +  eight  cents  =  1  dime  + cents. 

Five  yards  and  2  feet  are  how  many  feet  ?  - 

My  brother  is  17  years  old.     How  old  was  he  8  years 


If  sugar  is  5^  a  pound,  how  many  pounds  can  you  buy 
with  a  dime  and  a  nickel? 

A  string  17  ft.  long  was  cut  in  two  in  the  middle.  What 
was  the  length  of  each  part?  Find  by  measuring. 

How  many  gallons  of  oil  at  8  cents  a  gallon  can  you 
buy  with  17  cents?  How  many  cents  left  over? 

Eighteen. 


129.      Ten  and  eight,  or  1  ten  and  8  ones,  are  -     — . 

Nine  dots  and  nine  dots  are  how  many  dots? 

If-  nine  dots  are  taken  from  18  dots,  how  many  will 
remain  ? 

How  many  small  dots  are  on  the  card?  How  many  sixes 
do  you  see  on  it?  How  many  threes?  How  many  nines? 

Find  how  many  twos  make  eighteen. 

One-half  of  18  dots  is  -      -  dots. 

One-third  of  18  dots  is  -      -  dots. 

Two-thirds  of  18  dots  are  -      -  dots. 

Make  dots  for  the  following:  18,  6,  12,  9,  J  of  18. 

Count  to  18  by  2's.     By  3's.     By  6's. 

Is  18  an  even  or  an  odd  number? 

How  many  2's  in  18?    How  many  3's?    How  many  6's? 

How  many  9's  can  you  take  from  18?  Then  how  many 
9's  are  in  18? 


EIGHTEEN. 


93 


Take  18  sticks  and  find  how  many  8's  in  18,  and  how 
many  left  over. 

What  part  of  18  is  9?    What  part  of  18  is  6? 


« 

'/s 

* 

equal  parts.    Show 


130.  The  circle  is  divided  into  - 
me  one-sixth  (4)  of  the  circle. 

To  find  4  of  anything  we  must  divide  it  into equal 

parts. 

Show  me  4  of  the  dots  on  the  card, 
i  of  12  dots  =         -  dots. 
How  many  sixths  of  the  dots  are  large? 
.  f  of  12  dots  -  -  dots. 

|  of  12  dots  -          -  dots. 
Is  J  of  the  rectangle  as  much  as  -f  of  it? 
Is  \  of  12  dots  as  many  as  f  of  them? 
Find  4  of  12  dots  and  compare  it  with  f  of  them. 
Which  is  larger,  4  of  12  or  4  of  12? 
Show  me  4  of  18  blocks.    4  of  18  = 
What  part  of  12  is  2?     Of  6  is  1? 

131.  Copy  and  complete: 

9  +  9=  9X2=          18^-6=        18  —  (    )  =  9 

2X9=          18  H-  3  =          18 -*-  9  =        8  +  8  +  2  = 

18  —  9=          18-^2=  3X6=        6  X  (    )  =  18 


10  = 
4  = 

i  of  18  = 

\  of  18  = 

f  of  18 
|  of  18 

6  = 
5  = 

f  of  18  = 
|  of  18  = 

1+  i 
1-  1 

94: 


SCHOOL    ARITHMETIC. 


132.  A  boy  bought  2  books  at  9  cents  apiece.  They 
cost  him  -  -  cents. 

Barnet  put  18  nuts  on  a  fence.  A  squirrel  carried  off 
2  of  them  each  day  for  —  —  days.  Then  all  were  gone. 

How  many  days  are  2  weeks  and  4  days? 

Four  bushels  and  2  pecks,  or  4f  bu.,  are  -      -  pecks. 

Draw  a  line  18  in.  long.     Show  that  it  is  -      -  ft.  long. 

Mary  sold  eggs  at  a  cent  apiece.  How  much  did  she 
get  for  a  dozen  and  a  half? 

Find  the  cost  of  a  gallon  of  milk  at  4^  a  quart. 

If  1  orange  costs  2  cents,  what  will  9  oranges  cost? 

How  many  yards  in  a  piece  of  cloth  18  feet  long? 

I  want  to  buy  a  book  for  18  cents.  I  have  a  dime.  I 
need —  cents  more. 

Maud  has  18  jacks.  She  gave  |  of  them  to  Jane.  How 
many  had  she  left? 

How  many  squares  can  you  make  with  18  splints?  How 
many  triangles? 

Nineteen. 


133.      One  ten  and  9  ones,  or  10  and  9,  are  -    — . 
How  many  dots  are  2X9  dots,  and  1  dot? 
How  many  dots  are  6X3  dots,  and  1  dot? 
Nineteen  dots  are  how  many  more  than  3X6  dots? 
How  many  tens  in  19?    How  many  ones  left  over? 
How  many  2's  in  19,  and  how  many  ones  left  over? 
How  many  9's  in  19,  and  how  many  left  over? 


REVIEW    AND    DRILL.  95 

Show  that  10  is less  than  .19. 

Nineteen  is  how  many  more  than  11? 
Show  that  12  and  -     -  are  19. 
Show  that  19  is  -      -  more  than  13. 
To  each  of  the  following  add  the  number  that  will  make 
the  sum  19:     8,  11,  7,  9,  15,  17,  16. 

134.      Copy  and  complete: 

10+9=-         9  +  9  +  1-  8  +  8  +  3  = 

19—9=  2X9  +  1=  2X8  +  3  = 

19 -=-10=       19  -f-  9          =         19-^-8          = 


Review  and  Drill. 
135. 


a 

I 

c 

11  +  1  = 

12  +  2  = 

13  +  3 

11  +  3  = 

12  +  4  = 

13  +  5 

11  +  2  = 

12  +  6  = 

13  +  6 

11  +  5  = 

12  +  3  = 

14  +  5 

11  +  4  = 

12  +  5  = 

14  +  4 

11  +  7  = 

12  +  7  = 

14  +  2 

11  +  6  = 

13  +  2  = 

14  +  3 

11  +  8=  13  +  4=  15  +  2  = 

d                           e  f 

15  +  3=  9  +  3=  8  +  9  = 
15+4=  9  +  5=  9  +  9  = 

16  +  3=  9  +  4=  8  +  5  = 

16  +  2=  9  +  6=  8  +  8  = 

17  +  2=  9  +  7=  8  +  4  = 


96  SCHOOL    ARITHMETIC. 


9 

o  ~~  f~  o  —  •  — 

0     1     fj  

8  +  8  = 
7  +  4  = 
7  +  6  = 
7  +  5  = 
7  +  3  = 
7  +  7  = 

6 
6 
6 
6 
6 
5 
5 
5 

^      t 

+2=      5+5= 
+4=      4+4= 
+6=      4+2= 
+3=      4+3= 
+  5  =      3  +  4  = 
+4=      3+2= 
+2=      7+9= 
+3=      8+7= 

j 

fc 

i 

m 

2 

X 

2  = 

2 

X  8  = 

3 

X  5  = 

5 

X 

3 

2 

X 

3  = 

2 

X  9  = 

3 

X  6  = 

6 

X 

2 

2 

X 

4  = 

2 

X  10  = 

4 

X  2  = 

6 

X 

3 

2 

X 

5  = 

3 

X  2  = 

4 

X  3  = 

7 

X 

2 

2 

X 

6  — 

3 

X  3  = 

4 

X  4  = 

8 

X 

2 

2 

X 

7  = 

3 

X  4  = 

5 

X  2  = 

9 

X 

2 

n 

0 

P 

g 

9 

— 

2  = 

8 

2  = 

7 

o  — 

10 

— 

2 

9 

— 

7  = 

8 

6  = 

7 

o  

10 

— 

8 

9 

— 

3  = 

8 

o  — 

7 

4  = 

10 

— 

3 

9 

— 

6  = 

8 

—  5  = 

6 

—  2  = 

10 

— 

7 

9 

— 

4  = 

8 

4  = 

6 

4  = 

10 

— 

4 

9 

— 

O  "  -  -1 

7 

—  2  = 

6 

—  3  = 

10 

— 

3 

r 

s 

i 

u 

10 

— 

5  = 

12 

o  

13 

—  2  = 

14 

— 

2 

11 

— 

2  = 

12 

-10  = 

13 

-11  = 

14 

— 

3 

11 

— 

9  = 

12 

3  = 

13 

Q   

14 

— 

4 

11 

— 

o  

12 

Q  

13 

—  4  = 

14 

— 

5 

11 

— 

o  

12 

—  4  = 

13 

9  = 

14 

— 

9 

11 

— 

4  = 

12 

—  8  = 

13 

—  5  = 

14 

— 

6 

11 

— 

J-r  

12 

—  5  = 

13 

—  8  = 

14 

— 

8 

11 

— 

5  = 

12 

Y  — 

13 

6  = 

14 

— 

7 

11 

— 

6  = 

12 

—  $  = 

13 

-  7- 

14 

— 

10 

REVIEW    AND    DKILL. 


97 


V 

w 

4- 

Q    

14- 

-    2 

9- 

-  0  

16- 

-    2 

6- 

-2-= 

18- 

-    2 

8- 

-2  = 

4  - 

-    4 

10- 

-2  = 

— 

-    4 

12- 

-2  = 

1*2- 

-    4 

X 

¥ 

12- 

-    6=. 

18- 

-    3 

18- 

-    6  = 

10- 

-    5 

6- 

-    3  = 

15- 

-    5 

9- 

-    3  = 

12- 

-    6 

12- 

Q     

18- 

-    6 

15- 

-    3  = 

14- 

-   7 

136.  A  farmer  has  7  Jersey  cows  and  8  Durham 
cows.  How  many  cows  has  he? 

Willie  caught  1  trout  and  Harry  caught  9  trout.  How 
many  did  both  catch? 

School  begins  at  9  o'clock  in  the  morning,  and  continues 
3  hours.  What  time  is  it  when  school  is  dismissed? 

In  a  game  of  baseball  9  persons  play  on  each  side.  How 
many  players  are  there  in  the  game? 

A  table  is  6  feet  long  and  3  feet  wide.  What  is  the 
number  of  feet  around  it? 

From  a  dozen  and  a  half  cans  of  peaches  3  cans  were 
used.  How  many  cans  were  left? 

A  farmer  had  19  lambs  and  sold  7  of  them.  How  many 
lambs  had  he  left? 

One  sash  of  a  window  has  2  rows  of  panes,  and  3  panes 
in  a  row.  How  many  panes  are  there  in  the  sash? 

Hunter  has  8  rabbits;  Jack  has  half  as  many.  How 
many  rabbits  have  both  together? 

How  many  legs  have  6  three-legged  stools? 

From  a  brood  of  19  chickens,  6  were  sold,  and  half  a 
dozen  were  eaten.  How  many  chickens  were  left? 

How  many  times  does  the  sun  rise  and  set  in  1  week? 

Divide  18  peaches  among  6  girls.  How  many  peaches 
does  each  receive? 


*7 


98 


9OHOOL   ARITHMETIC. 


A  plank  is  18  inches  long.  If  you  saw  off  a  Half  foot, 
how  long  is  the  plank  then? 

Make  a  rectangle  5  inches  long  and  3  inches  wide,  and 
divide  it  into  inch  squares.  How  many  square  inches  in 
the  rectangle? 

How  many  quart  bottles  will  it  take  to  hold  16  pints? 

If  you  have  |  of  a  dollar  and  spend  J,  how  many  fourths 
have  you  left?  How  many  quarters? 

Nineteen  ounces  are  how  many  more  ounces  than  one 
pound? 

Draw  a  line  17  inches  long.  How  many  more  inches  long 
is  it  than  1  foot? 

How  many  strokes  will  a  clock  make  in  striking  8  and  9  ? 


1 

2 

3 

4 

5 

I 

3 

4 

1 

fwe 

nt; 

tn 

F* 

I) 

( 

137.      Ten  and  ten,  or  two  tens,  are . 

How    many  squares  in   the   upper   row?     How  many 
rows  are  there?    How  many  squares  in  all  the  rows? 

Then  4  times  5  squares  are squares. 

Show  that  5  times  4  squares  are  20  squares. 

Two  tens  are  as  many  as fives  or fours. 

Find  from  the  card  how  many  twos  in  twenty. 
What  does  the  figure  0  mean  in  the  number  20? 
What  figure  shows  that  there  are  two  10's  in  twenty? 
Show  that  20  is  more  than  10. 


TWENTY.  99 

Show  that  16  is  -       -  less  than  20. 
Show  that  — —  is  5  less  than  20. 

One-half  of  20  dots  is  dots. 

Two  dots  are  found  in  20  dots  -     -  times. 

One-fourth  of  20  squares  is  squares. 

Two-fourths  of  20  squares  are  squares. 

Three-fourths  of  20  squares  are  squares. 

138.      One-half  of  anything  is  one  of  its  two  equal  parts. 

One-third  of  anything  is  one  of  its equal  parts. 

What  is  meant  by  i  of  anything?     J? 

Divide   10  blocks    into   10  equal    parts.     How  many 
blocks  in  each  part? 

What  is  one  of  the  equal  parts  called?    (One-tenth.) 

One- tenth  of  10  blocks  is block. 

How  many  ones  make  one  ten?     Then  one  one  is  what 
part  of  one  ten? 

Show  me  one-tenth  (TV)  of  20  dots. 

One  cent  is  what  part  of  10  cents?     One  is  what  part 
of  10? 

Draw  a  line  10  inches  long.     Under  it  draw  a  line  T^ 
as  long. 

Into  how  many  equal  parts  is  this  circle 
divided? 

What  is  each  part  called? 

How  many  tenths  are  dark?    How  many 
are  light? 

T3¥  of  the  circle   -f-  -^  of  the  circle    =    of  the 

circle,  or  the  whole  circle. 

How  many  tenths  are  -fa  and  ^  ? 

Make  two  rows  of  10  dots  each.     Draw  a  ring  around 
•j-V  of  the  dots.     Draw  a  ring  around  |  of  the  20  dots. 


100  SCHOOL    ARITHMETIC. 

"Which  is  more,  |  of  20  dots  or  ^  of  20  dots  ?'" 

If  you  take  T3¥  of  anything  away,  how  many  tenths 
remain  ? 

One  of  the  ten  equal  parts  of  anything  is  called  one-tenth. 

What  are  3  of  the  parts  called?  Four  of  the  parts? 
Seven  of  the  parts? 

How  many  tenths  are  there  in  anything?  How  many 
halves?  Show  that  J  =  •&. 

One  tenth  means  one  out  of  ten.   What  does  -£$  mean  ? 

A?   W 

How  many  dimes  make  a  dollar?  A  dime  is  what  part 
of  a  dollar? 

What  part  of  a  dollar  are  3  dimes?    5  dimes? 

Is  one  half-dollar  as  much  as  5  dimes? 

Is  onejhalf  as  much  as  5  tenths? 

Twenty  things  are  sometimes  called  a  score.  How  many 
things  in  half  a  score  ?  In  -^  of  a  score  2 

139.     Complete  the  process: 


10  +  10  = 

20  —  10  = 

20  =  10  + 

18+2  = 

20-      2  = 

20  -=18  + 

16+4  = 

20-      4  = 

20  =F  16  + 

17+3  = 

20-      3  = 

20  =  17  + 

15+5  = 

20-      5  = 

20  =  15  + 

14+    6  = 

20-      6  = 

20  ==  14  + 

12+8  = 

20-      8  = 

20  ==  12  + 

13+7  = 

20-     7  = 

20  =  13  + 

2X10  = 

20  -f-  10  = 

4  of  20  = 

10  X    2  = 

20^-2  = 

i  of  20  = 

4X    5  = 

20-^-5  = 

i  of  20  = 

5X4  = 

20  -f-    4  = 

TV  of  20  = 

TWENTY. 


140.      10  is  contained  in  20 times  and over. 

9  is  contained  in  20 times  and over. 

8  is  contained  in  20 times  and over. 

7  is  contained  in  20 times  and  -  —  over. 

6  is  contained  in  20 times  and over. 

5  is  contained  in  20 times  and  -     -  over. 

3  is  contained  in  20 times  and over. 

4  is  contained  in  20 times  and over. 

2  is  contained  in  20 times  and 


141.  Count  by  fives  to  20.  -  fives  are  20. 
Count  by  twos  to  20.         —  twos  are  20. 
Count  by  fours  to  20.    •     —  fours  are  20. 

Count  by  threes  to  18.  threes  and  2  are  20. 

Count  by  sixes  to  18.         —  sixes  and  2  are  20. 
Count  by  tens  to  10^.         —  tens  are  100. 

142.  How    many    shoes    will    be    required  to  shoe  5 
horses?     10  men? 

If  you  had  10  cents  and  your  mother  gave  you  a  ten- 
cent  piece,  how  much  money  would  you  have? 

A  farmer  owns  3  horses,  8  cows,  and  9  sheep.  How 
many  animals  has  he? 

If  a  strip  of  paper  is  5  inches  long  and  4  inches  wide, 
how  many  square  inches  does  it  contain? 

Two  dimes  equal  how  many  nickels? 

If  20  bananas  were  divided  equally  among  4  girls,  how 
many  would  each  have? 

If  a  strip  of  paper  contains  20  square  inches,  and  it  is 
5  inches  long,  how  wide  is  it? 

Marvin  had  20  cents  and  spent  i  of  them  for  ink,  and 
the  rest  for  paper.  What  did  the  paper  cost? 


102 


SCHOOL    ARITHMETIC. 


How  many  school  days  in  4  weeks? 

If  I  cut  5  apples  into  quarters,  to  how  many  children 
can  I  give  a  piece? 

Is  20  odd  or  even?  How  much  must  you  add  to  it  to 
make  it  odd? 

Take  20  cents  and  give  -^  of  them  to  each  of  5  of  your 
classmates.  How  many  have  you  left  ? 

Draw  11  vertical  lines  2  inches  apart  on  the  blackboard. 
How  far  apart  are  the  two  outside  lines? 

Harry  had  20  marbles.  He  put  i  of  them  into  one  pile, 
£  of  them  into  another  pile,  and  the  rest  in  the  third  pile. 
How  many  in  each  pile? 

Eggs  are  10^  a  dozen.  How  many  dozen  can  be  bought 
for  2(#? 

We  have  found  out  that  X  stands  for  10.  What  do  you 
think  XX  stands  for? 

How  many  years  are  3  score  years  ? 

How  old  is  a  man  who  is  3  score  and  ten  years  of  age? 

Numbers  to  100. 


=21.     10+10+5=25.     10+10+10=30.     10+10+10+4=34. 


143.  Here  t  stands  for  the  tens.  What  does  o  stand  for? 
Draw  squares  like  these  to  represent  23,  27,  36,  39. 
Draw  squares  to  represent  2  £  +  6  o,  3  £  +  8  o,  2  /  +  2  £. 


NUMBERS   TO   100. 


103 


Complete: 

20  +  1    =21  20  +  8=  25  =  22+50 

20  +  2    =  30  +  1    =  26  = 

20  +  4  30  +  3    =  32  = 

20  +  6    =  30  +  5    =  37  = 

22+6o=  32  +  50=  39  = 

5  t  +  3  t  =  8  t  =  80      6  o  +  5  o  =  llo  =  12  +  lo,  or  11 


J 


10+10+10+10+10+6=56. 


10+10+10+10+3=43. 


144.     Draw  squares  to  represent  45,  57,  52,  64,  66. 
Draw  squares  to  represent  4£+6  o,  5£  +  8  o,  6  £+1  £• 


104 

Complete : 

40  +  1  =  41 

40  +  4  = 

50  +  0  = 
50  +  5  = 
50  +  9  = 
60  +  3  = 
60  +  8  = 

42  =  4  £  +  2< 

45  = 

47  = 

53  = 

56  = 

58  = 

64  = 

67  = 


SCHOOL    ARITHMETIC. 


4  t  +  1  o  =41  o  41  =  4  t  +  1  o 

4  t  +  4  o  =  44  = 

4  *  +  8  o  =  48  = 
5£  +  Oc=  50  = 

5  t  +  5  o  =  55  = 
5£  +  9o  =  59  = 

6  *  +  3  0  =  63  = 
Gt  +  8o  =  68  = 

18  o  +  3  o  =  21  o  =  2  J  +  1  o,  or  21 
15  o  +  50  = 

30  o  +  2  0  = 
40  o  +  7  0  = 

60  o  +  5  o  = 


10+10+10+104-10+10+10+5=75. 


Draw  squares  to  represent  73,  84,  89,  92. 
Draw  squares  to  represent  7  t  +  4  o,  8  £  +  10  o, 


NUMBERS   TO    100.  105 

145.     Complete : 

70+    1  =  71  7£  +  10  =  7lo      71  =  7*  +  lo 

80+3=  8£  +  3o  =  83  = 

80+8=  8  £  +  80  =  88  = 

90+0=  9  £  +  00  =  90  = 

90+5='  9£  +  5o  =  95  = 

60  +  20=  6£+2£  =  80  = 

76  =  7  t  +  6  o  70  o  +    4  o  =  74  o  =  7  £+4o,  or  74 

79=  70o+7o  = 

81=  80  o+    5o  = 

87=  800  +  100  = 

93=  900+    3  o  = 

96  =  90  o  +  10  o  =  100  o  =10  t,  or  100 

1  dime    +  5^=15^  1 1-\-  5  o=15      12^=1  dime  +  2$ 

2  dimes  +  5^=  2^+50= 

4  dimes  +  2^=  4^+2  o= 

5  dimes  +  8^=  5^+80=          25^= 

7  dimes  +  5j=  7  t+  50=          38^=- 

8  dimes  +  7^=  8  £+  7  0=          53^= 

9  dimes  +  9^=  9  t-}-  9  o=          81tf= 
9  dimes  +10^=  9  ^+10  o=  98^= 


146.     Write  and  read  the  numbers  to  100. 
Count  backwards  from  20  to  0.     From  50  to  20. 
Count  by  2's  to  50;  then  backwards  to  2. 
Count  by  10's  from  0  to  100;  then  backwards  to  0. 
Count  by  10's  from  1  to  91.     .From  2  to  92. 
In  25  what  does  the  2  stand  for?     The  5? 
In  33  the  figures  are  alike.     Do  they  mean  the  same 
thing? 


106 

Complete : 

24=20 
27  = 
22  = 
31  = 
34  = 
39  = 


SCHOOL    ARITHMETIC. 


46  = 

48  = 
52  = 
55  = 
68  = 
71  = 


74 

77 
79 

82 
85 
87 


88 
89 
67 
94 
96 
99 


24  +  3=  32  +  4  = 

147.     Add: 


24 
3 


32 
4 


24 
4 


32 

5 


25  —  3  = 


21 


33 
4 


37  —  4  = 


33 
5 


34 

2 


26 
3 


35 
3 


46 

2 


44 
4 


51 

7 


62 
6 


65 
4 


52 
7 


74 
3 


83 
6 


77 
2 


86 
2 


94 
5 


NUMBERS  TO  100. 


107 


Subtract: 

25 
3 


37 

4 


26 

2 


47 
4 


36 

2 


35 
3 


19 
4 


29 
4 


39 

4 


49 
4 


59 
4 


69 
4 


79 
4 


28 
5 


38 
5 


48 
5 


57 
3 


67 
3 


77 
3 


87 
3 


Name  results  quickly: 


21  +  1  = 

21  +  2  = 

21  +  3 

81  +  1  = 

31  +  2  = 

31  +  3 

41  +  1  = 

51  +  2  = 

41  +  3 

51  +  1  = 

71  +  2  = 

51  +  3 

71  +  1  = 

22  +  2  = 

22  +  3 

91  +  1  = 

32  +  2  = 

32  +  3 

61  +  1  = 

42  +  2  = 

42  +  3 

81  +  1  = 

52  +  2  = 

52  +  3 

21  +  4 

31  +  4 

41  +  4 

51  +  4 

22  +  4 

32  +  4 

42  +  4 

52  +  4 


If  you  add  1  to  numbers  ending  in  1?  with  what  figure 
does  the  sum  end? 

If  you  add  2  to  numbers  ending  in  1,  with  what  figure 
does  the  sum  end? 

If  you  add  2  to  numbers  ending  in  2,  with  what  figure 
does  the  sum  end?  ' 

If  you  add  3  to  numbers  ending  in  1?  with  what  figure 
does  the  sum  end? 

If  you  add  3  to  numbers  ending  in  2,  with  what  figure 
does  the  sum  end? 


108  SCHOOL   ARITHMETIC. 

« 

If  you  add  4  to  numbers  ending  in  2;  with  what  figure 
does  the  sum  end? 

If  you  add  4  to  numbers  ending  in  3,  with  what  figure 
does  the  sum  end? 

When  you  increase  31  by  2?  do  you  add  2  to  the  1  or 
to  the  3? 


21  +  5  = 

21  +  6  = 

21  +  7  = 

21+8  = 

31  +  5  = 

31  +  6  = 

31  +  7  = 

31+8  = 

41  +  5  = 

41  +  6  = 

41  +  7  = 

51+8  = 

51  +  5  = 

51  +  6  = 

51  +  7  = 

71+8  = 

22  +  5  = 

22  +  6  = 

22  +  7  = 

73  +  6  = 

32  +  5  = 

32  +  6  = 

32  +  7  = 

84  +  5  = 

42  +  5  = 

42  +  6  = 

42  +  7  = 

92+7  = 

52  +  5  = 

52  +  6  = 

52  +  7  = 

65  +  3  = 

If  you  subtract  1  from  numbers  ending  in  2,  with  what 
figure  does  each  answer  end? 

If  you  subtract  1  from  numbers  ending  in  3,  with  what 
figure  does  each  answer  end? 

Add  3  to  numbers  ending  in  5.  What  is  the  ending 
figure  ? 

Subtract  5  from  numbers  ending  in  8.  What  is  the 
ending  figure? 

Find  the  value  of : 


24- 

1 

26 

-3 

87 

—  4 

49 

—  7 

16 

—  5 

34- 

1 

46 

-3 

18 

—  5 

79 

-7 

26 

-5 

74- 

1 

86 

-3 

28 

—  5 

88 

-6 

66 

—  5 

15- 

2 

17 

-3 

48 

—  5 

58 

-6 

18 

—  8 

25  — 

2 

27 

-3 

19 

-6 

39 

—  8 

28 

g 

35- 

2 

57 

-3 

29 

-6 

28 

-3 

49 

—  9 

65- 

2 

77 

-4 

39 

-6 

47 

-4 

86 

-6 

16  — 

3 

97 

—  4 

89 

—  7 

56 

—  5 

99 

—  7 

ADDITION    AND    SUBTRACTION. 


109 


5 

15 

25 

35 

2 

45 

55 

65 

75 

6 

16 

26 

36 

3 

46 

56 

66 

76 

4 

14 

24 

34 

4 

44 

54 

64 

74 

Add  numbers  in  center  of  each  square  to  each  of  the 
other  numbers.  Subtract  central  number  from  each  of  the 
others. 

Addition  and  Subtraction. 


20  +  15 


14  +  22 


31  +  26 


148.     If  we  put  these  splints  all  together,  how  many 
loose  splints  will  we  have?     How  many  bundles,  or  tens? 


20  =  2  t  +  0  o 
15  =  1  *  +  5  o 


=  3£  +  50 


31  = 


Four  ones  and  2  ones  are  6  ones.  One  ten 
and  2  tens  are  3  tens.  Where  is  the  6 
written?  The  3?  Which  then  is  the  ones' 
place?  The  tens'  place? 

No  ones  and  5  ones  are  ones.     Two 

tens  and  1  ten  are tens.    Show  me  the 

5  ones  in  the  picture.  The  2  tens.  The  1 
ten.  The  3  tens.  Which  do  we  add  first— 
the  ones  or  the  tensf 

Show  me  the  6  ones  in  the  picture.  The 
7  ones.  The  3  tens.  The  2  tens.  The  5  tens. 


57  = 


HO  SCHOOL    ARITHMETIC. 

149.  Add: 

13  12  20        16  21  10  15  23 
24       13  11        22  15  12  23  14 

24       27  18       25  32  30  26  34 

14  31  31       42  24  10  32  33 

43       41  20       51  62  75  17  54 

26       28  40       31  25  23  82  35 

64       45  17       50  73  69  40  26 

23       53  42       40  16  20  50  72 

150.  Find  the  value  of: 


32  +  26 

12  +  14 

34  +  25 

15  +  10 

54+15 

36  +  23 

17  +  50 

25  +  10 

67  +  21 

60  +  15 

24  +  34 

35  +  10 

23  +  70 

54  +  33 

31  +  51 

12  +  12 

42  +  27 

62  +  17 

63  +  25 

24  +  12 

36  +  12 

41  +  24 

56  +  42 

36  +  12 

11  +  11 

70  +  16 

40  +  21 

22  +  11 

40  +  40 

50  +  31 

24+  12 

33  +  11 

A  boy  has  30  hens  and  12  roosters.  How  many  chickens 
has  he? 

A  man  paid  a  barber  25^  for  a  hair-cut  and  10^  for  a 
shave.  For  both  he  paid #. 

A  farmer  drove  14  miles  to  town  and  then  drove  home. 
How  far  did  he  drive? 

Helen's  papa  gave  her  50f5  and  her  marnma  gave  her 
a  quarter.  She  then  had cents. 


ADDITION   AND    SUBTRACTION. 


Ill 


There  are  24  hours  in  a  day.  In  two  days  there  are 
hours. 

There  were  20  cents  in  a  box,  when  George  put  in  14 
cents,  and  Ada  5  cents.  How  many  cents  were  in  the 
box  then? 

How  many  days  in  May  and  June  together? 

There  are  45  pupils  in  one  school  and  42  in  another. 
In  both  schools  there  are  —  -  pupils. 

Hallie's  book  has  23  pages  more  than  there  are  in  Odie's. 
There  are  42  pages  in  Odie's  book.  How  many  pages  are 
there  in  Hallie's  book? 

There  are  33  frogs  in  one  pond,  and  24  in  another.  How 
many  are  there  in  both? 


25  —  5  = 


36  —  4  = 


151.  Here  are  24  splints  (2  tens  and  4  ones).  Take 
4  away.  How  many  are  left? 

Did  you  take  the  4  from  the  loose  splints  (the  ones) 
or  from  the  tens?  How  many  ones  were  left? 


24  =  2  t  +  4  o 
4=  4o 


=  2^  +  50 
=  5o 


20  =  2  £+00  20  —  2  £  - 

Show  with  splints  how  many  16  —  6  are. 
Draw  squares  to  represent  18  —  8. 


112 


SCHOOL   ARITHMETIC. 


Show  me  3  tens  and  5  ones  with  splints.  Take  3  away 
and  tell  me  what  you  have  left. 

From  what  did  you  take  the  3  splints?  How  many 
ones  were  left?  How  many  tens? 


3=  3o 

32  =  3  t  +  2  o 


4:= 


4:0 


Show  with  splints  how  many  17  —  4  are. 
Draw  squares  to  represent  24  —  3. 

152.      Subtract: 


16 

26 

36 

46 

18 

28 

38 

48 

4 

4 

4 

4 

5 

5 

5 

5 

18 

27 

26 

37 

49 

68 

75 

89 

8 

3 

2 

4 

7 

3 

5 

a 

36  —  12    =       24. 

153.      Here  are  36  splints.     How  many  tens?     How 
many  ones? 

Take  away  12  splints  (2  ones  and  1  ten). 


ADDITION    AND    SUBTRACTION.  113 

How  many  ones  are  left?  How  many  tens?  How  many 
splints  ? 

Two  ones  from  6  ones  leaves ones.     One  ten  from  3  tens 

leaves tens.    Two  tens  and  4  ones  are .     Which  do 

24-        we  subtract  first — the  ones  or  the  tenst 

When  12  is  subtracted  from  36,  what  is  the  remainder? 
Show  me  the  squares  that  represent  it. 

Take  25  splints  (2  tens  and  5  ones.)  Take  away  13 
splints  (1  ten  and  3  ones).  How  many  ones  remain?  How 
many  tens?  How  many  splints?  25  —  13  = 

Draw  squares  to  represent  25  —  10. 

154.     Subtract: 

13  16    26    34    45    24    27    30 
2     4    14    14    12    12    15    10 

•  « 
37    44    56    63    58    76    69    75 

14  12    24    21    33    25    36    50 

86    93    77    68    84    50    95    98 
41    21    34    58    62    30    70    23 

80    72    97    48    59    76    81    99 
60    52    60    18    21    41    31    44 


114  SCHOOL    ARITHMETIC. 

23 

42          4  ones,  2  ones,  and  3  ones  are ones. 

14.          I  ten,    4  tens,  and  2  tens  are tens. 

—          The  sum  is tens  and ones,  or ." 

Find  the  sum: 

12  14  11  20  30  25  13  21 
24  31  42  45  27  40  35  16 
51  23  45  13  32  14  40  51 

23  27    18    25    32    30    26    34 
31    42    54    26    28    20    17    64 

24  30    21    11    31    13     2    10 

Jane  had  3  dimes  and  a  nickel.  She  gave  a  dime  and  a 
nickel  for  a  slate.  How  much  money  had  she  left  ? 

William  earned  45  cents  on  Friday  and  30  cents  on 
Saturday.  On  both  days  he  earned cents. 

There  are  24  hours  in  a  day.  If  you  work  10  hours, 
how  many  hours  do  you  have  for  rest? 

If  you  cut  12  feet  from  a  fish  line  36  feet  long,  how 
many  feet  of  line  will  be  left? 

This  week  there  are  69  pupils  in  school;  last  week  there 
were  48.  How  many  new  pupils  have  come  this  week? 

Eobert  had  40  cents,  Mack  had  30  cents,  and  Clyde 
had  10  cents  HOAV  many  more  cents  did  the  three  boys 
need  to  make  a  dollar? 

George  has  14  marbles  and  Tom  has  10  more.  They 
both  have marbles? 

The  white  hen  has  15  chicks,  and  the  black  hen  has  5 
less.  They  both  have  chicks. 

John  had  a  knife  worth  45  cents,  which  he  traded  to 
Walter  for  his  knife  and  2  nickels.  What  was  Walter's 
knife  worth? 


NUMBERS    TO    30. 


115 


Numbers  to  30. 


33333333 

156.  What  is  the  name  of  the  number  made  up  of  2 
tens  and  1? 

2  tens  and  2?  2  tens  and  3?  2  tens  and  4?  2  tens 
and  5?  2  tens  and  6?  2  tens  and  7?  2  tens  and  8?  2 
tens  and  9? 

How  many  squares  in  the  rectangle?  How  many 
threes?  Then  8  threes  are . 

How  many  squares  in  the  upper  row?  How  many 
rows?  Then  3X8  squares  = squares. 

Show  that  8X3  squares  =  3X8  squares. 

The  dark  row  is  what  part  of  the  rectangle?  One  part 
out  of  8  parts  is  called  one . 

Show  how  many  eighths  of  the  rectangle  make  J  of  it. 

•J  of  24  squares  =  -      -  squares, 
•f-  of  24  squares  =  -  —  squares. 

i  of  24  squares  =  squares. 

\  of  the  rectangle  =  -   — squares. 

The  upper  row  is  what  part  of  the  rectangle? 


of  24  squares  = 
of  24  squares  = 


How  many  light  squares  are   there? 
make  21?    How  many  7's? 


squares, 
squares. 

How  many  3's 


\  of  21  squares  =  -      -  squares, 
f  of  21  squares  = squares. 


116  SCHOOL    ARITHMETIC. 

Make  4  dots  six  times.     How  many  dots  have  you? 

•  •    •    •    •    How  many  4's  make  24? 

•  •    •    •    •        Arrange  5  rows  of  5  dots  each  in  «  square, 

•  •    •    •    •    as  in  the  number  picture  at  the  left.      Tell 

•  •    •    •    •    how  many  5's  in  25. 

•  •    •    •    •         Count  by  5's  to  25.     5  X  5  =       — . 
Make   3  dots   9   times.      How  many 

dots  have  you?  How  many  3's  make 
27?  How  many  9' s? 

Show  by  the  picture  at  the  right  that 
4X7  dots  ==7X4  dots. 

How  many  4's  in  28  ?    How  many  7's  in  28  ? 

Count  by  3's  to  30.     How  many  3's  make  30? 

156.  Complete  and  memorize: 

1X3  =  3.  3X1  =  3. 

2X3=  3X2  = 

3X3=  3X3  = 

4X3=  3X4  = 

5X3=  3X5  = 

6X3=  3X6  = 

7X3=  3X7  = 

8X3=  3  X    8  = 

9X3=  3X9  = 

10  X  3  =  3  X  10  = 

157.  3  squares  are  found  in  18  squares  -  -  times. 
3  squares  are  found  in  24  squares  -  -  times. 
3  squares  are  found  in  30  squares  -  -  times. 
3  squares  are  found  in  21  squares  —  -  times. 

What  added  to  2  tens  makes  22?     23?     26?     29? 
Find  1  of  22  splints.    J  of  22  =  -    — . 
How  many  elevens  make  22? 
Find  how  many  12's  make  24? 


NUMBERS   TO    30. 

158.     Find  the  value  of: 


117 


9- 

-3 

30- 

-3 

20- 

-2 

15- 

-3 

27- 

-3 

24- 

-2 

12- 

-  3 

12- 

-  2 

22- 

-2 

18- 

-3 

18- 

-2 

20- 

-3 

24- 

-3 

16- 

-2 

16- 

-3 

21- 

-3 

14- 

-2 

22- 

-3 

20 
40 

60 
50 
30 

80 


10 
10 
10 
10 
10 
10 


4  / 
4> 
5> 

6> 
91 

^   D  - 

<7  = 

25-4- 

28- 

OPC 

-  D  — 

-7  = 

t  oi 
iof 

4  of 

iof 
-1-of 
iof 

4nf 

Zl  

24  = 

O'T 

zo 
28 
27 
26 
29 
30 
9^ 

—  10 

=  20 
01 

T  - 

j  

1 

f  b  — 

z/b 

OA 

5  — 

A 

A  (  - 
O/i 

oo 

i 
4_ 

4:  

Ij 

Zi*± 
00 

^•±  

OQ      •- 

01 

1 
J_ 

zi 

C)A 

8- 

ZiO 
C)A 

4O 

ore 

—  on 

1    ~ 
4^ 

Zl1! 

9ft 

K  — 

A*± 

9ft 

\  — 

^it) 

94-  — 

—  19 

1 
4-. 

159.     Find  the  cost  of  10  pints  of  milk  at  3^  a  pint. 

A  boy  walks  3  miles  a  day.  In  7  days  he  walks 

miles. 

A  man  who  had  24  bushels  of  potatoes  sold  J  of  them. 
How  many  had  he  left? 

Mr.  Jones  had  27  sheep  but  3  of  them  died.  He  then 
had sheep  left. 

What  will  2  dozen  eggs  cost  at  a  cent  apiece? 

How  many  ounces  in  i  of  a  pound?    In  |  of  a  pound? 

A  blacksmith  has  24  horseshoes.  He  can  shoe  • 

horses  with  them. 

With  25  cents  I  can  buy  -  -  3-cent  stamps,  and  I  shall 
have left. 

A  man  had  $30.  He  gave  TV  of  it  for  a  pair  of  shoes. 
Find  the  cost  of  the  shoes. 


118 


SCHOOL   ARITHMETIC. 


A  room  is  27  feet  long.     How  many  yards  long  is  it? 

Divide  21  apples  equally  among  3  boys.  How  many 
apples  will  each  boy  have? 

If  you  have  25  oranges,  how  many  times  can  you  give 
away  oranges  if  you  give  5  each  time? 

If  it  takes  4  men  7  days  to  dig  a  certain  ditch,  how  long 
will  it  take  1  man  to  dig  the  ditch? 

How  many  weeks  are  there  in  28  days? 

If  you  sleep  8  hours  every  day,  what  part  of  the  whole 
day  do  you  sleep?  In  1  day  there  are  -  -  hours. 

How  many  days  has  February?  When  a  week  of  this 
month  has  passed,  how  many  days  of  it  will  be  left? 


1 

2 

3 

4 

5 

6 

7 

How  many  squares  in  the  upper  row  of  this  rectangle? 
How  many  rows? 

3X7   squares  =  -       -  squares. 

Draw  a  rectangle  7  inches  long  and  3  inches  wide.  Draw 
lines  to  divide  it  into  square  inches. 

How  many  sq.  in.  in  1  row?    How  many  rows? 
3  X  7  sq.  in.  = sq.  in. 

Find  how  many  square  inches  in  each  of  the  following: 

A  square,  5  inches  on  a  side. 
A  rectangle,  6  inches  by  4  inches. 
A  rectangle,  7  inches  by  4  inches. 
A  rectangle,  10  inches  by  3  inches. 


NUMBERS    TO    30.  119 


160.  In  this  picture  the  line  jib  is  a  vertical  line. 
Which  other  lines  are  vertical? 

The  line  mn  is  a  horizontal  line.  Point  out  the  other 
horizontal  lines. 

Draw  on  the  blackboard  a  square  3  feet  on  each  side. 
Draw  two  horizontal  lines  to  divide  it  into  3  equal  parts. 

Then  draw  two  vertical  lines  to  divide  it  into  9  equal 
parts.  How  long  is  each  of  the  9  parts?  How  wide? 

What  is  the  shape  of  each  part? 

A  square  that  is  a  foot  on  each  side  is  called  a  square 
foot  (sq.  ft.). 

How  many  square  feet  are  there  in  your  large  square? 

Measure  the  large  square  with  the  yardstick.  What  is 
the  length  in  yards?  The  width? 

A  square  that  is  a  yard  on  each  side  is  called  a  square 
yard  (sq.  yd.). 

Kow  who  can  tell  how  many  square  feet  in  a  square 
yard? 

In  3  square  yards  there  are  square  feet. 

A  rug  is  5  ft.  square.     How  many  square  feet  in  it? 

A  strip  of  carpet  is  9  yards  long  and  1  yard  wide.  It 
contains  -  -  square  yards. 

There  are  4  strips  of  carpet  on  our  bedroom.  Each 
strip  is  5  yards  long  and  a  yard  wide.  How  many  square 
yards  of  carpet  are  there? 


120 


SCHOOL    ARITHMETIC. 


Numbers  to  40. 


444444:4:44:4 

161.      What  is  the  name  of  the  number  made  up  of  3 
tens  and  1?     3  tens  and  2?     3  tens  and  3? 

Head  the  numbers:   34;     35;     36;     37;     38;     39. 
In  5  rows  of  6  dots  each  there  are dots. 


5X6  = 


6  X  5  = 


30  H-  5  = 
—  dots. 


In  5  rows  of  7  dots  each  there  are  — 

5  times  7  are  -    — .  7  times  5  are  -    — . 

Show  by  the  dots  at  the  right  how  many  7's  in  35.  How 
many  5's  in  35? 

How  many  squares  in  this  rectangle?  How  many  tens? 
How  many  fours? 

Show  that  4  X  10  squares  =  10  X  4  squares. 

The  upper  row  is  what  part  of  the  rectangle?  Then 
1  of  40  squares  is squares. 

The  left-hand  column  is  what  part  of  the  rectangle? 
then  -^  of  40  squares  is squares. 

162.  How  many  squares  are  there  in  7  columns  ?  Then 
7X4  squares  are  -  -  squares. 

Make  4  rows  of  7  dots  each.    How  many  dots? 

How  many  4?s  make  28?    How  many  7's? 

Draw  a  ring  around  i  of  the  dots.    J  of  28  = . 


NUMBERS    TO   40.  121 

163.  How  many  squares  are  there  in  8  columns?    Then 
8X4  are  -     -  squares. 

Here  are  32  blocks.  Give  me  i  of  them,  i  of  32  = . 

Now  divide  these  32  blocks  into  4  equal  parts.     How 
many  in  each  part?    i  of  32  =       — . 

164.  How    many    squares  in  1  column  ?     How  many 
columns  are  light?    How  many  squares  are  light? 

9X4  squares  =          -  squares.      9X4=        — . 

Divide  36  splints  into  4  equal  piles.    How  many  splints 
in  each  pile? 

36  splints  -r-  4  =  -     -  splints. 

Separate  36  splints    into  9  equal    piles.     How    many 
splints  in  each  pile? 

36  splints  -T-  9  = splints. 

Lay  3.6  blocks  in  3  equal  rows.     How  many  3's  make 
36?    How  many  12's? 

Make  a  square  of  dots,  having  six  dots  on  each  side. 

In  6  rows  of  6  dots  each  there  are  dots. 

Count  by  4's  to  36.     Count  by  6's  to  36. 
Count  by  4's  to  40.     How  many  4's  make  40? 

165.  Complete  and  memorize: 

1X4  =  4.  4X1  =  4. 

2X4=  4X    2  = 

3X4=  .4X3  = 

4X4=  4X    4  = 

5  X4=  4X5  = 

6X4=  4X6  = 

7X4  =  4X    7  = 

8  X4=  4X8  = 

9X4=  4X9  = 

10X4=  4X10  = 


122 


SCHOOL   AEITHMETIC. 


times, 
times, 
times, 
times. 


166.  4  squares  are  contained  in  24  squares  - 
4  squares  are  contained  in  32  squares  - 
4  squares  are  contained  in  28  squares  — 
4  squares  are  contained  in  36  squares  - 

Show  by  dots  how  many  3's  make  33.   How  many  ll's? 

1  of  33  dots  —         -  dots. 
What  added  to  3  tens  makes  34?    37? 

Count  by  3's  from  0  to  36,  then  backwards  to  3. 

Count  by  4's  from  0  to  40,  then  backwards  to  4. 

Count  by  3's  from  1  to  37,  then  backwards  to  1. 

Count  by  4's  from  1  to  41,  then  backwards  to  1. 

Count  by  4's  from  2  to  38,  then  backwards  to  2. 

167.  Find  the  value  of: 


8- 

-4 

32- 

-4 

28- 

-2 

30-^3 

16- 

-4 

36- 

-4 

26- 

-2 

40-^2 

12- 

-4 

40- 

-4 

34- 

-2 

iof40 

20- 

-4 

32- 

-2 

24- 

-2 

4  of  36 

28- 

-4 

36- 

-2 

33- 

-3 

i  of  40 

24- 

-4 

30- 

-2 

36- 

-3 

iof  36 

5  X  6  —  30  —  6  —  £  of  30  =  37  —  (  )  X  4  + 

5X7—  32  —  8—  i  of  30  —  81  =  (  )  X  ±,-+ 

6X6—  35  —  7—  Jof35—  34—  (  )  X  4  + 

5X5—  36  —  9—  iof36—  38—  (  )  X  4 + 

168.  Our  hens  lay  4  eggs  a  day.  How  many  will  they 
lay  in  10  days? 

How  many  quarts  in  6  gal.  ?    In  9  gal.  ? 

How  many  months  in  2  yr.?    In  3  yr.?  In  \  of  a  year? 

I  have  4  rows  of  peach  trees,  8  in  each  row.  How  many 
trees  have  I? 

Mr.  Wilson  has  11  barrels  of  apples,  3  bushels  in  each 
barrel.  He  has bushels  of  apples. 


NUMBERS    TO    50.  123 

In  35  days  there  are  -      -  weeks. 

How  many  cents  are  6  five-cent  pieces? 

How  many  eggs  are  there  in  3  dozen  eggs? 

From  the  8th  to  the  29th  of  May  there  are  -  -  days, 
or  —  -  weeks. 

How  many  inches  long  is  the  yard-stick? 

A  line  is  3  feet  2  inches  long.     How  many  inches  is  it? 

John  took  3 6. pecks  of  potatoes  to  the  store.  How  many 
bushels  was  that? 

How  many  5-cent  stamps  can  you  buy  for  30  cents? 

A  farmer  has  32  horses.  How  many  4-horse  teams  can 
he  form? 

At  5  cents  a  ride,  how  many  street-car  rides  can  be 
taken  for  30  cents? 

Mr.  Henry  gave  30  cents  to  his  children.  Each  child 
got  a  dime.  How  many  children  has  he? 

A  bushel  of  oats  weighs  32  pounds.  How  much  does 
a  peck  weigh? 

Eight  quarts  make  a  peck.  How  many  quarts  in  a 
bushel?  4  X  8  qt.  =  -  qt. 

Numbers  to  50. 


169.  How  many  dots  do  you  see  here?  How  many 
fives? 

10   X     5  dots  =  dots. 

5   X   10  dots  =  dots. 

Find  from  the  picture  how  many  5  times  5  dots  are. 
6  times  5  dots.  8  times  5  dots.  7  times  5  dots.  9  times 
5  dots. 

Count  by  5's  from  5  to  50,  then  backwards  to  5. 


124 


SCHOOL   ARITHMETIC. 


Complete  and  memorize: 

1  five  =5. 

2  fives  = 

3  fives  = 

4  fives  = 

5  fives  = 

6  fives  = 

7  fives  = 

8  fives  = 

9  fives  = 
10  fives  = 

!Find  the  value  of: 

4X5  +  5  5X4+6 

5X5  +  3  7X4  +  2 

7X5  +  1  8X3  +  5 

8X5  +  2  9X4  +  2 


5  blocks  are  conl 
blocks. 

5  blocks  are  conl 
blocks. 

5  pegs  are  contained  in  30 
pegs. 

5  inches  are  conta 

5  is  contained  in     5 

5  is  contained  in  10 

5  is  contained  in  20 

5  is  contained  in  25 

5  is  contained  in  40 

5  is  contained  in  50 

5  is  contained  in  45 

Point  out  one  of  the  5  equal  parts  of  50  dots. 


1  X5  =  5. 

5X    1  =  5. 

2X5  = 

5X  -2=*= 

3X5  = 

5X3  = 

4X5  = 

5  X    4  = 

5X5  = 

5X5  = 

6X5  = 

5X6  = 

7X5  = 

5X    7  = 

8  X  5  = 

5X8  = 

9X5  = 

5X    9  = 

10  X  5  = 

5  X  10  = 

4  of  24     i 

1            P    C\f\ 

t  oi  20 

f  of  20 

4  of  21      8 

•     •     •     •     • 

y  times  —     5 

id  in  15       6 

J      •           r\  * 

id  m  25 

8 

•     •     •     •     • 

A 

in     ^fl 

111    OU 

in  10  inches 

i 

one    time. 

5  —  5  =  . 

,  • 

-  times. 

times. 

,  • 

OK           K  - 

times. 

KA             K 

Ov           £>       -        ' 

A&           Z  : 

NUMBERS    TO    50. 


125 


171.      Is  i  of  50  dots  the  same  as  50  dots  -f-  5  ?  Prove  it. 
How  much  is  i  of  25  cents?    |  of  25  cents? 


How  many  dots  in  each  row  of  dots  at  the  left? 

How  many  rows  are  there? 

In  6  rows  of  7  dots  each  there  are dots. 

i    /\  0 .  O  /\    i  . 

Add  to  42  by  6's.     How  many  6's  in  42? 
Add  to  42  by  7's.     How  many  7's  in  42? 

In  6  rows  of  8  dots  each  there  are dots. 

By  aid  of  the  middle  picture,  complete: 
6X8= .8X6=       — .  48-^6=       — .  48-f-8= 

In  a  square  made  of  dots,  7  dots  on  each  side, 
are dots. 

7X7=       — . 
172.      Copy  and  complete: 


there 


50.-T-  5  = 
30-^-5  = 
40-^5  = 
20 -=-5  = 

25  -r-  5  = 
45  -i-  5  = 

40  -f-  8  = 
45-:-9  = 
40 -=-4  = 
48-^-6  = 


35  —  5  = 
15  —  5  = 
17  —  5  = 
21  —  5  = 

28  —  5  = 
32  —  5  = 

6X7  = 
7X  7  = 
8X5  = 
4X  9  = 


"±t7      .       4    -                  . 

50  —  10  =         -jV  of  50  = 

30- 

-10  = 

^  of  50  — 

40- 

-10  = 

|  of  50  = 

20- 

-10  = 

^  of  50  = 

25- 

-10  = 

i  of  50  = 

45- 

-10  = 

|  of  50  = 

42- 

-7  = 

6X8  = 

42- 

-6  = 

7X    6  = 

48- 

-8  = 

4X10  = 

49- 

-7  = 

41-J-    5  — 

126 


SCHOOL    ARITHMETIC. 


173.      How  many  cents  are  6  nickels  worth? 

Our  cow  gives  10  quarts  of  milk  a  day.  In  5  days  she 
gives  quarts. 

How  many  flags  at  5  cents  apiece  can  I  buy  for  17  cents? 
How  many  cents  shall  I  have  left? 


For  17  cents  I  can  buy  -      -  flags.     I  shall  have 

cents  left. 

How  many  5-cent  stamps  can  I  buy  for  30^?  Draw 
the  picture. 

Forty  pecks  of  onions  are  how  many  bushels? 
A  house  is  12  yards  long.     It  is  -     -  feet  long. 
At  6  dollars  a  ton,  how  many  tons  of  coal  can  be  bought 
for  42  dollars? 

What  will  7  yards  of  cloth  cost  at  7  cents  a  yard? 
A  pansy  has  five  petals.    How  many  petals  do  9  pansies 
have? 

How  many  times  can  a  5-inch  line  be  measured  off  on 
a  line  40  inches  long? 

Ben  had  30  cents  and  gave  J  of  it  for  candy.  How  much 
money  had  he  left?  Show  by  drawing. 

What  are  3  dozen  eggs  worth  at  1  cent  apiece? 

What  will  a  pound  and  a  half  of  butter  cost  at  16  cents 
a  pound? 

Draw  a  rectangle  10  inches  long  and  4  inches  wide. 
Divide  it  into  square  inches.  How  many  are  there? 

How  many  rows  are  there  running  lengthwise? 

How  many  inch  squares  in  each  row? 

How  many  square  inches,  then,  are  4  times  10  square 
inches  ? 


ADDITION    AND    SUBTRACTION. 


127 


Find  the  number  of  square  inches  in  the  following: 

A  square,  measuring  7  inches  on  a  side. 
A  rectangle,  10  inches  by  5  inches. 
A  rectangle,  10  inches  by  4  inches. 
A  rectangle,  9  inches  by  5  inches. 

9  square  feet  make  1  square  yard.     How  many  square 
yards  are  there  in  45  sq.  ft.? 

Addition  and  Subtraction. 


1«  -f-  90  +  1  o    =    2*  -f  Oo 
19  +  1  =    20 

174.    Take  19  splints.     Make  a  bundle  of  10.     How 
many  do  you  need  to  make  another  ten? 


19  •  =  It 
1  = 


lo 


29  =  2  t 
1  = 


9  o 
lo 


20  =  2  £  +  0  o  30  =  3  £  +  0  o 

Show  with  splints  how  many  39  and  1  are.     49  and  1. 
Add: 


49 

1 


59 
1 


79 
1 


89 
1 


69 
1 


99 
1 


How  many  splints  must  you  put  with  18  to  make  2  tens? 
With  28  to  make  3  tens? 


18  = 

2  = 


20 


28  =  2^  +  80 
2  =  20 


128 


SCHOOL    ARITHMETIC. 


Show  with  splints  how  many  38  and  2  are.    48  and  2. 
Add: 

38         48         78         58         88         68      '   98 

2222222 

Name  results  quickly: 


9  +  1 

28  +  2 

59  +  1 

78  +  2 

8  +  2 

39  +  1 

58  +  2 

89  +  1 

19  +  1 

38  +  2 

69  +  1 

88  +  2 

18  +  2 

49  +  1 

68  +  2 

99  +  1 

29  +  1 

48  +  2 

79  +  1 

98  +  2 

How  many  tens  in  one  hundred?     How  many  tens  in 
half  a  hundred?    How  many  ones? 

J  of  100  = tens,  or  ones. 


9  +  2    = 


19  +  2    = 


175.      Nine  splints  and  2  splints  are 
Nineteen  splints  and  2  splints  are  - 


splints. 


—  splints. 

Take  one  splint  from  the  two  and  put  it  with  the  nine. 
You  now  have  1  ten  and  1  one,  or . 

Take  one  splint  from  the  other  two  and  put  it  with 
the  nine.  You  now  have tens  and  -  —  one,  or . 


Show  by  splints  how  many  29  and  2  are. 
49  and  2. 


19 

2 


29 

2 


39 

2 


49 

2 


59 

2 


69 

2 


39  and  2. 

79 

2 


ADDITION    AND    SUBTRACTION.  129 

176.  Take  11  splints  (a  ten  and  a  one).  How  can  you 
take  2  splints  away  from  the  11?  How  many  must  you 
take  from  the  ten?  How  many  will  be  left? 

Take  21  splints — 2  tens  and  a  one.  Take  away  2  splints. 
Ho\v  many  must  you  take  from  one  of  the  tens?  How 
many  tens  and  how  many  ones  will  be  left? 

Show  by  splints  how  many  31  less  2  are.  41  —  2. 
51—2.  61  —  2. 


11    21 

31    41 

51 

61 

71 

81 

2     2 

2     2 

2 

2 

2 

2 

~9 

177.  Find 

the  value  of: 

9  +  2 

8  +  2 

11 

—  2 

10- 

2 

19  +  2 

18  +  2 

21 

2 

20  — 

2 

39  +  2 

48  +  2 

41 

—  2 

30  — 

2 

49  +  2 

28  +  2 

61 

—  2 

50  — 

2 

29  +  2 

68  +  2 

31 

—  2 

60  — 

2 

69  +  2 

38  +  2 

51 

—  2 

40- 

2 

89  +  2 

58  +  2 

71 

—  2 

70- 

2 

79  +  2 

78  +  2 

81 

2i 

90  — 

2 

59  +  2 

98  +  2 

91 

—  2 

80  — 

2 

Add  by  2's  from  2  to  50. 
Subtract  by  2's  from  40  to  18. 
Add  by  2's  from  9  to  61. 
Subtract  by  2's  from  49  to  9. 


130 


SCHOOL    ARITHMETIC. 


8  +  3 


17  +  4 


19 


178.     Show   with   blocks   that   8  +  3  =   1    ten   and   1 


one,  or  11. 


Show  that  18  +  3  = 
Show  that  28  +  3  = 
Show  that  17  +  4  = 
Show  that  19  +  3  = 


tens  and 
tens  and 
tens  and 
tens  and 


one,  or 
one,  or 
one,  or 
ones,  or 


179.  How  many  squares  do  you  see  in  the  picture  at 
the  left?  How  many  of  them  will  be  left  if  you  take 
away  the  3  dark  ones? 

How  many  squares  in  the  next  picture?  How  many 
light  ones? 

1   ten  and        8  ones,  or  18. 

—  tens  and        8  ones,  or  -    — . 

—  ten  and ones,  or . 


Show  that  21  —  3  = 
Show  that  31  —  3  = 
Show  that  21  —  4  — 
Show  that  22  --  3  = 


ten  and 


Add;  also,  subtract: 


11 
3 


21 
3 


31 
3 


41 
3 


61 
3 


81 
3 


ones,  or 


71 
3 


51 
3 


ADDITION    AND    SUBTRACTION.  131 


21 

31 

41 

51 

71 

61 

91 

81 

4 

4 

4 

4 

4 

4 

4 

4 

22 

32 

42 

62 

52 

72 

82 

92 

3 

3 

3 

3 

3 

3 

3 

3 

180. 

N 

ame  results  at 

sight  : 

- 

8 

+ 

3 

.    7 

+ 

4 

11 

g 

11- 

4 

18 

+ 

3 

17 

+ 

4 

21 

—  3 

21—4 

28 

+ 

3 

27 

+ 

4 

31 

—  3 

31- 

4 

58 

+ 

3 

37 

+ 

4 

51 

—  3 

41- 

4 

48 

+ 

3 

67 

+ 

4 

61 

—  3 

61—4 

68 

+ 

3 

87 

+ 

4 

41 

-3 

81- 

4 

38 

+ 

3 

47 

+ 

4 

81 

-3 

71- 

4 

88 

+ 

3 

57 

+ 

4 

71 

-3 

51- 

4 

78 

+ 

3 

77 

+ 

4 

91 

-3 

91- 

4 

Add  by  3's  from  0 

to 

51 

.    From 

2  to  50 

Subtract 

by 

4's  from  48 

to  0.     From  45 

to  1. 

181. 

Name 

results  at  sight: 

8 

+ 

4 

9 

+ 

4 

12 

-4 

13- 

4 

18 

+ 

4 

19 

+ 

4 

22 

A 

23  — 

4 

28 

+ 

4 

29 

+ 

4 

32 

-4 

43- 

4 

38 

+ 

4 

49 

+ 

4 

42 

-4 

53  — 

4 

48 

+ 

4 

39 

+ 

4 

62 

-4 

33  — 

4 

68 

+ 

4 

79 

+ 

4 

82 

4 

73  — 

4 

88 

+ 

4 

89 

+ 

4 

52 

-4 

93  — 

4 

78 

+ 

4 

69 

+ 

4 

72 

-4 

63  — 

4 

58 

+ 

4 

59 

+ 

4 

92 

—  4 

83  — 

4 

Add  5  to  16,  26,  36,  46,  56,  66,  76,  86. 
Subtract  5  from  21,  31,  41,  51,  61,  71,  81,  91 


132 


SCHOOL    ARITHMETIC. 


15     +     7    =  19 

182.      Find  the  sum  of  15  and  7. 


15      = 


Write  15  and  then  write  the   7  ones  under  the  5  ones.          15 
7  ones  and  5  ones  are  -    -  ones,  or  1  ten  and  2  ones.  1 

Write  the  2  ones  in  ones'  place  under  7.  22 

What  shall  be  done  with  the  ten  ?    Add  it  to  the  1  ten  in 

15.     1  ten  and  1  ten  are tens. 

In  what  place  do  we  write  the  tens  ? 


Find  the  sum  of  19  and  15. 

5  ones  -\-  9  ones  =  14  ones,  or  1  ten  and  4  ones. 
1  ten  +  1  ten  -f-  1  ten  = tens. 


Copy  and 

add: 

18    38 

29 

4     4 

15 

25    35 

27 

56    48 

16 

63    42 

74 

28    39 

17 

32 
19 

64 

18 

31 

49 


63 

28 

43 
32 

28 
64 


42 
39 

57 
25 

36 

58 


19 
15 

34 


78 
14 

68 
17 

43 
37 


69 
24 

34 

38 

54 
39 


ADDITION    AND  SUBTRACTION.                               133 

26  57         44         87  65  39  76  58 

58  27         37         15  26  47  18  37 

15  16         23          14  26  32  29  40 

23  34         42         37  38  18  29  27 

47  26         18         25  14  47  30  19 

183.  Find  the  value  of: 


36  +  14 

25  +  45 

33  +  49 

26  +  35  +  18 

33  +  17 

81  +  19 

62  +  28 

17  +  23  +  46 

42  +  18 

46  +  37 

71  +  29 

35  +  18  +  26 

82  +  18 

34  +  58 

80  +  18 

24  +  39  +  27 

47  +  14  76  +  17  46  +  35  31  +  17  +  46 

184.  There  are  31  days  in  May  and  30  in  June.  In 
both  months  there  are  -  -  days. 

Mr.  Jones  has  58  sheep  in  one  field  and  37  in  another. 
In  both  fields  he  has  -  -  sheep. 

Ella  is  18  years  old  and  her  mother  is  36  years  older. 
How  old  is  her  mother? 

Our  black  horse  cost  $65  and  our  red  cow  cost  $25. 
How  much  did  both  cost? 

If  a  room  is  18  feet  long  and  16  feet  wide,  how  many 
feet  is  it  around  the  room? 

A  Christmas  tree  held  13  dolls.  27  balls,  37  flags,  and 
17  bags.  How  many  articles  were  there  in  all? 

Edith  paid  35  cents  for  a  book,  15  cents  for  paper,  and 
3  cents  for  a  ruler.  How  much  did  they  all  cost  her? 

Mr.  White's  wagon  cost  $42.  His  buggy  cost  $29  more 
than  the  wagon.  How  much  did  the  buggy  cost? 

How  many  days  are  there  in  October,  November,  and 
December? 


134 


SCHOOL    ARITHMETIC. 


2t 


2o    — 


22     —     5      = 


185.  Take  22  splints  (2  tens  and  2  ones).  How  many 
ones  can  you  take  away  without  taking  any  from  a  bundle  ? 

If  you  wish  to  take  5  splints  away,  how  many  ones  must 
you  take  from  one  of  the  tens?  How  many  ones  will  be 
left?  One  ten  and  7  ones  are  -  — . 

Take  32  splints  (3  tens  and  2  ones).  How  can  you  take 
7  splints  away?  Can  you  take  7  ones  from  the  2  ones? 

Take  the  string  from  one  of  the  bundles.  Xow  how 
many  ones  have  you?  Take  7  splints  away.  How  many 
ones  are  left  ?  How  many  tens  ? 


22  =  2 
5  = 

t  + 

2 
5 

0  = 

+ 

12 

5 

0. 
0. 

n  = 

7 

0 

17  = 

=  lt 

+ 

7 

0. 

25  = 

7  o  =  7  o. 


=  2£+  50. 


How  many  squares  do  you  see  in  the  picture  ? 
How  many  tens?  How  many  ones? 

We  cannot  take  5  squares  from  the  3 
squares,  so  we  must  take  one  of  the  tens  and 
and  put  it  with  the  3  ones,  making  13  ones. 
We  then  have  2  tens  and  13  ones.  What  is 
left  when  5  ones  are  taken  away? 

Show  with  splints  how  many  23  less  5  are. 
31  less  7. 


ADDITION    AND    SUBTRACTION. 


Subtract : 

24         25 
6 


32 


26 

8 


21 

n 


34 


35 


31 


16 


15 


We  cannot  take  6  from  1,  so  we  put  one  of  the  tens  with 
the  1,  and  take  6  from  11.  There  are  only  2  tens  left, 
so  we  take  the  1  ten  from  2  tens. 

31  =  =  20  +  11 
16  =  :  10+    6 


15  =  10+    5 

NOTE. — Of  course,  as  soon  as  the  pupils  understand  the  process, 
they  should  do  the  work  without  any  change  of  figures. 

Show  with  splints  how  to  subtract  12  from  31.  15  from 
32.  Use  splints  to  show  how  many  25  less  15  are.  45 
less  20. 

186.      Copy  and  subtract: 

23          31          34         42          63          54         36         75 
8  6          16         25          34         28          19         47 


60 
29 


91 
16 


40 
25 


53 
15 


68 
35 


90 
50 


84 
30 


93 

48 


44 

28 


55 
37 


64 
26 


45 

28 


74 
24 


80 
51 


100 
50 


100 
80 


44 

—  19 

52 

—  27 

41  — 

16 

50 

-38 

75 

-36 

5"2  — 

27 

72 

—  22 

44 

-18 

63- 

38 

67 

—  28 

63 

-45 

74- 

49 

83 

-38 

81 

-50 

85  — 

56 

62 

-43 

27 

9 

96- 

67 

91 

•—56 

50 

—  13 

43  — 

15 

136  SCHOOL    ARITHMETIC. 

187.  Find  the  value  of: 
34  —  16 

42  —  15 
61  —  24 
83  —  15 
21  —  12 
75  —  54 
92  —  65 

188.  How  many  more  days  are  there  in  this  month?' 
A  man  wants  to  buy  a  watch  for  $32.    He  has  only  $25. 

How  much  more  does  he  need? 

Julia  bought  a  doll  for  29  cents,  and  gave  the  store- 
keeper a  half-dollar.  How  much  change  did  she  get? 

In  a  school  there  are  45  pupils.  There  are  26  boys. 
How  many  girls  are  there? 

What  number  must  you  add  to  14  to  get  21? 

What  number  must  you  subtract  from  32  to  get  24? 

A  man  paid  $94  for  a  horse  and  cart.  He  paid  $18 
for  the  cart  and  $ —  -  for  the  horse. 

Grandma  is  83  years  old,  and  Lizzie  is  7  years  old.  How 
much  older  is  grandma  than  Lizzie? 

If  your  mamma  had  2  dozen  eggs,  and  used  all  of  them 
at  Easter  but  a  half-dozen,  how  many  did  she  use? 

How  many  days  from  the  llth  of  June  to  the  9th  of 
July? 

A  barrel  of  oil  contained  53  gallons  but  5  gallons  leaked 
out.  There  were  -  -  gallons  left  in. 

Mrs.  Hill  had  62  hens.     She  sold  27  of  them  and  had 

—  left. 

Tom  weighs  96  pounds  and  Warren  78  pounds.  How 
many  more  pounds  does  Tom  weigh  than  Warren? 


NUMBERS   TO    SIXTY.  137 

Numbers  to  Sixty. 


189.  How  many  dots  in  the  picture?    How  many  rows 
of  10  dots  each? 

6  X  10  dots  -          -  dots. 

How  many  large  dots  do  you  see?  How  many  sixes  are 
there? 

10  X  6  dots  =          -  dots. 
In  60  there  are  —     -  tens  or  —     -  sixes. 
How  many  times  can  you  take  10  dots  from  60  dots? 
00  dots  -f-  10  dots  =  -     -  times. 

The  large  dots  are  what  part  of  the  60  dots?  TV  of  60 
dots  = dots. 

How  many  tenths  of  the  60  dots  equal  \  of  the  60  dots? 
Ten  dots  are  what  part  of  60  dots?    \  of  60  dots  = 
dots. 

How  many  sixths  of  60  equal  i  of  60? 

In  60  there  are twelves. 

In  60  there  are fives. 

190.  How  many  small  dots  in  the  picture?    How  many 
rows  of  9  dots  each?    How  many  columns  of  6  dots  each? 

6X9  dots  =          -  dots.    9X6  dots  =          -  dots. 

Draw  a  rectangle  9  inches  long  and  6  inches  wide,  and 
draw  horizontal  and  vertical  lines  to  divide  it  into  square 
inches. 


138  SCHOOL    ARITHMETIC. 

How  many  squares  inches  does  it  contain?  How  many 
times  6  sq.  in.  ?  How  many  times  9  sq.  in.  ? 

How  many  sq.  in.  in  one-sixth  of  the  rectangle?  i  of 
54  =  -  — .  54  sq.  in.  -r-  6  = sq.  in. 

In  -J-  of  the  rectangle  how  many  sq.  in.  ?  -Jof  54  = 
.  54  sq.  in.  ~-  9  =  sq.  in. 

Show  how  many  sixths  of  the  rectangle  equal  i  of  it. 

Count  by  4's  to  60.     By  5's.     By  6's. 

191.       Complete  and  memorize: 


1 

six     =  6 

1 

X 

6  —  6. 

6 

X 

1  =  6. 

2 

sixes  = 

2 

X 

6  = 

6 

X 

2  = 

3 

sixes  = 

3 

X 

6  = 

6 

X 

r>   

4 

sixes  = 

4 

X 

6== 

6 

X 

4  = 

5 

sixes  = 

5 

X 

6  = 

6 

X 

5  = 

6 

sixes  = 

6 

X 

6  = 

6 

X 

6  = 

7 

sixes  = 

7 

X 

6  = 

6 

X 

7  = 

8 

sixes  = 

8 

X 

6  = 

6 

X 

8  = 

9 

sixes  = 

9 

X 

6  = 

6 

X 

9  = 

10 

sixes  = 

10 

X 

6  = 

6 

X 

10  = 

192,      Find  how  many  times: 

6  dots  are  contained  in  18  dots. 

6  squares  are  contained  in  30  squares 

6  eggs  are  contained  in  48  eggs. 

6  blocks  are  contained  in  36  blocks. 

6  inches  are  contained  in  42  inches. 

6  beans  are  contained  in  54  beans. 

6  feet  are  contained  in  24  feet. 

9  sq.  ft.  are  contained  in  36  sq.  ft. 

9  sq.  ft.  are  contained  in  54  sq.  ft. 

9  dollars  are  contained  in  45  dollars. 


NUMBERS    TO    SIXTY. 


139 


193.      In   7   rows  of  8   squares   each 
there  are  -      -  squares. 

How  many  times  7  squares  make  56 
squares  ? 

Show  that  7X8  squares  =  =  8X7 
squares. 

How  many  times  are  8  squares  found  in  the  56  squares? 
7  squares? 

56  squares  *-r-  8  squares  =  -  times.     56  squares 

-r-  7  squares  =  -     -  times. 

What  part  of  the  rectangle  is  found  in  the  upper  row? 

Two  rows  are  what  part  of  the  rectangle?    Three  rows? 

Four-sevenths  of  56  squares  are  -      -  squares. 

Seven  squares  are  what  part  of  the  56  squares?     14 
squares  ? 

Compare  f  of  the  squares  with  i  of  them. 

56  squares  -r-  8  =  —     —  squares.     56  squares  -r-  7  = 
squares. 

How  many  9's  in  56,  and  how  many  over? 

How  many  5's  in  56,  and  how  many  over? 

How  many  10's  in  56,  and  how  many  over? 

Find  the  value  of: 


12- 

-6 

4 

X 

7 

t 

of 

60 

60  = 

7X 

8  + 

(  )• 

30- 

-6 

6 

X 

8 

1 

of 

60 

53  = 

10  X 

5  + 

()• 

48- 

-6 

7 

X 

7 

3 
f 

of 

60 

54- 

7X 

T  + 

()• 

42- 

-6 

4 

X 

8 

1 

of 

60 

K  Q 
OO    = 

8  X 

7  + 

(  )• 

54- 

-6 

3 

X 

9 

i 

of 

21 

55  = 

6X 

9  + 

(  )• 

36- 

-6 

5 

X 

8 

t 

of 

40 

59  = 

11  X 

5  + 

()• 

24- 

-6 

7 

X 

5 

j 

of 

60 

51  = 

8  X 

6  + 

(  )• 

60-^-6 

5 

X 

9 

1 

of 

60 

52  = 

6  X 

8  + 

(  ). 

140 


SCHOOL   ARITHMETIC. 


194.  Here  is  a  picture  of  a  watch 
face. 

When  the  pointer  in  the  little 
circle  has  gone  round  once,  how  many 
minutes  have  passed? 

The  little  circle  is  divided  into  how 
many  spaces? 

Sixty  seconds  make  a  minute. 

"When  the  longer  hand  in  the  large  circle  has  gone  round 
once,  what  time  has  passed? 

Into  how  many  spaces  is  the  large  circle  divided? 
Sixty  minutes  make  an  hour. 

Which  is  the  hour-hand?  Which  the  minute-hand? 
The  second-hand? 

How  often  does  the  hour-hand  go  round  from  midnight 
to  midnight? 

Then  how  many  hours  make  a  day? 

What  time  of  day  is  shown  on  the  watch-face? 

How  many  minutes  in  a  half  of  an  hour?  In  a  quarter 
of  an  hour? 

What  part  of  an  hour  are  30  minutes?  15  minutes?  10 
minutes  ? 

From  noon  to  midnight  is  what  part  of  48  hours? 

In  half  a  minute  how  many  seconds? 

What  part  of  a  minute  are  15  seconds?  10  seconds? 
6  seconds? 

In  what  time  does  the  hour-hand  go  round  four  times? 

How  many  hours  in  a  half  of  a  day? 

How  many  hours  is  it  from  6  A.  M.  on  Monday  till 
6  A.  M.  on  Tuesday? 


NUMBERS    TO    SIXTY.  141 

195.  How  much  money  will  buy  10  pounds  of  sugar 
at  6  cents  a  pound? 

Five  boys  bought  a  ball  for  50  cents.  No  one  gave 
more  money  than  another.  How  much  did  each  give? 

In  8  weeks  there  are days. 

We  had  48  eggs  on  Sunday.  On  Monday  we  got  a 
dozen  more.  How  many  eggs  had  we  then?  How  many 
dozens  ? 

9  quarts  of  milk  at  6  cents  a  quart  will  cost  —   -  cents. 

Maud  had  11  nickels.  She  gave  50  cents  for  a  doll,  and 
had  -  -  cents  left. 

A  house  is  30  feet  long  and  18  feet  wide.  What  is  the 
distance  around  the  house? 

A  rug  is  9  feet  long  and  6  feet  wide.  It  contains 

square  feet,  or square  yards. 

There  are  52  weeks  in  a  year.  How  many  weeks  in 
half  a  year? 

A  bushel  of  wheat  weighs  60  pounds.  What  is  the 
weight  of  a  peck?  A  half -bushel? 

Six  windows  contain  48  panes  of  glass.  How  many 
panes  are  there  in  each  window? 

If  each  of  7  boys  makes  8  balls  of  snow,  how  many  will 
they  have  together? 

Roy  borrowed  60  cents  from  his  brother,  and  paid  him 
back  6  cents  of  it  every  week.  How  many  weeks  did  it 
take  to  pay  the  whole? 

If  a  man  works  8  hours  a  day,  what  part  of  the  day 
does  he  work? 

If  a  horse  walks  a  mile  in  15  minutes,  how  many  miles 
at  that  rate  will  he  walk  in  an  hour? 

If  a  railway  train  runs  one  mile  in  2  minutes,  how  many 
miles  will  it  go  in  an  hour? 


142  SCHOOL    ARITHMETIC. 

Numbers  to  Seventy. 


196.  We  have  -       -  rows  of  10  dots  each;  there  are 
dots  in  all  the  rows.     7  X  10  dots  =  -      -  dots. 

There  are  10  columns  of  -      -  dots  each.     10  X  Y  dots 

= dots. 

We  see  that  there  are  -      -  tens  or  -      -  sevens  in  YO. 

YO  -r- 10  =  YO  -r-  Y  = 

The  large  dots  are  one  -  -  of  the  YO  dots.  TV  of  YO  = 
The  small  dots  are  nine  -  -  of  the  YO  dots.  T9^of  Y0=r 
On  one  side  of  the  vertical  line  there  are  -  -  tenths 

of  the  YO  dots]  on  the  other  side  we  find  J  of  the  YO  dots. 

One  side  has  as  many  dots  as  the  other.     (-J-  =  y-g-.) 

197.  There  are  -     -  small  dots  in  the  picture — seven 
rows  of  -      -  dots  each.     Y  X  9  dots  ==  -     -  dots. 

There  are  9  columns  of  -   —  dots  each.     9  X  Y  dots  = 

dots. 

We  can  take  Y  small  dots  away  -       -  times;  we  can 
take  away  9  small  dots  - —   -  times. 

63  dots  -f-  Y  dots  =          -  times.     63  dots  -^  9  dots  = 

times. 

Show  by  a  drawing  that  9  sevens  =  Y  nines. 
Count  by  5's  to  YO.    By  10's.    By  Y's, 


NUMBERS    TO    SEVENTY. 


143 


198.      Complete  and  memorize: 


.1  seven  =  7, 

2  sevens  = 

3  sevens  = 

4  sevens  = 

5  sevens  = 

6  sevens  ==• 

7  sevens  = 

8  sevens  = 

9  sevens  = 
10  sevens  = 


1X7  =  7. 
2X7  = 
3X7  = 
4X7  = 
5X7  = 
6X7  = 
7X7  = 
8X7  = 
9X7  = 
10  X  7  = 


7X 

7X 
X 
X 
X 
X 
X 
X 
X 


7  X  10  = 


199.      7  dots  are  contained  in  21   dots  -       -  times. 
7  days  are  contained  in  70  days  -      -  times. 
7  pints  are  contained  in  35  pints  -       -  times. 
7  yards  are  contained  in  63  yards  -     -  times. 
9  sq.  ft.  are  contained  in  36  sq.  ft.  -      -  times. 
9  eggs  are  contained  in  63  eggs  -      -  times. 
7  pounds  are  contained  in  66  pounds  -      -  times,  and 
3  pounds  over. 


6 


200.  Here  is  a  square.  How 
many  small  squares  in  the  upper 
row?  How  many  rows? 

8X8  squares  ===  -     -  squares. 

How  many  times  can  8  squares 
be  found  in  the  64  squares? 

In  one-half  of  the  large  square  how  many  small  squares  ? 
i  of  64  squares  =  -      -  squares. 
64  squares  -r-  2  =  -       -  squares. 
64  squares  -r-  8  =  squares, 


144  SCHOOL    ARITHMETIC. 

The  upper  row  is  what  part  of  the  large  square? 
How  many  eighths  of  the  large  square  are  on  each  side 
of  the  dark  line? 

•J   of   64   squares   -  -  squares. 

-f    of   64   squares   —  -       -  squares. 

201.  Find  the  value  of: 

14  —  7  7X6  iof64  64=    9X    7  +  (  ). 

28  —  7  9X5  £  of  64  62  =  .7  X    8  +  (  ). 

35  —  7  8X7  f  of  64  69  =    8  X    8  +  (  ). 

21  —  7  7X9  A  of  70  68  =    7  X    9  +  (  ). 

70  —  7  8X8  A  of  70  61  =    8  X    7  +  (  ). 

42  —  7  6X7  iV  of  70  67  =  10  X    7  —  (  ). 

49  —  7  9X6  A  of  70  65-=    6  X'10  +  (  ). 

56  —  7  6X8  \  of  70  66  =    7  X  10  —  (  ). 

63  —  7  9X7  -f-  of  70  70  =    8  X    8  +  (  ). 

202.  In  10  weeks  there  are  -     -  days. 

Tom  has  65  cents.     How  much  more  than  50^  is  that? 

Maria  has  40  cents  and  Martha  has  a  quarter.  How 
much  have  they  both? 

At  8  cents  a  quart  how  much  will  8  quarts  of  chestnuts 
cost? 

How  much  will  3  yards  of  wire  cost  at  7  cents  a  foot? 

10  cents  is  \  of  my  money.     How  much  have  I? 

A  nickel  is  \  of  my  money.     How  much  have  I? 

I  gave  A  °^  my  money  for  a  5-cent  stamp.  How  much 
had  I? 

7  children  give  9  cents  each  to  a  Children's  Aid  Society. 
How  much  money  is  given  by  all  together? 


NUMBERS    TO    EIGHTY. 


145 


In  a  school-room  there  are  63  seats  arranged  in  7  rows. 
How  many  seats  in  each  row? 

Robert  has  56  cents.  How  many  quarts  of  peanuts  can 
he  buy  at  7  cents  a  quart? 

How  old  is  a  man  who  has  lived  3  score  and  10  years? 


Numbers  to  Eighty. 
10 


8 

203.  How  many  squares  in  this  rectangle?  How  many 
rows  of  10  squares  each?  How  many  columns  of  8  squares 
each?  8'X  10=  10  X  8  = 

Find  how  many  squares  in  9  columns.  9X8=  8X9== 
How  often  do  80  squares  contain  10  squares?  SO-^-1011^ 
How  many  times  are  8  squares  contained  in  80  squares? 
How  many  tens  make  80?  How  many  tens  make  i  of  80? 

^  of  80  =  |  of  80  = 

How  many  8's  make  80?    How  many  8's  make  \  of  80? 
Which  is  more,  T5¥  of  80  or  %  of  80  I 
Make  6  rows  of  12  dots  each,,  and  tell  how  many  six 
12's  are.     12  X  6  = 

Show  that  9  X  8  =  6  X  12. 

In  50  there  are  -     -  5's;  in  25  there  are 5's. 

Count  by  6's  to  78.     By  7's  to  77. 
Count  by  8's  to  80.     By  5's  to  80, 
*io 


146  SCHOOL    ARITHMETIC 


204.   Complete  and  memorize: 

1 

eight   =8 

1 

X 

8  =  8 

8 

X 

1  =  8 

2 

eights  = 

2 

X 

o   

8 

X 

'2=  . 

3 

eights  = 

3 

X 

8  = 

8 

X 

?  = 

4 

eights  = 

4 

X 

8  = 

8 

X 

4  = 

5 

eights  = 

5 

X 

Q     

8 

X 

5  = 

6 

eights  = 

6 

X 

8  = 

8 

X 

6  = 

7 

eights  = 

7 

X 

8  = 

8 

X 

7  = 

8 

eights  = 

8 

X 

8  = 

8 

X 

8  = 

9 

eights  = 

9 

X 

o  

8 

X 

9  = 

10 

eights  = 

10 

X 

8  = 

8 

X 

10  = 

205.  Find  how  many  times : 

8   squares   are  contained  in   24  squares. 

8   squares  are   contained  in  40   squares. 

8  squares   are  contained  in   72   squares. 

9  squares   are  contained  in   72   squares. 

6  pegs  are  contained  in  66  pegs. 

7  days  are  contained  in  77   days. 

8  pounds  are   contained  in   64  pounds. 

206.  Find  the  value  of: 

16  —  8           5X7           I  of  36  75=    7X10  + () 

32  —  8           4X9           f  of  36  72  =      9  X    8  +  (  ) 

40  —  8           6X8           iof40  76  =    8  X    9  +  (  ) 

80  —  8          7X9          |  of  40  71  =    8  X    8  +  (  ) 

72  —  8           8X8           f  of  40  74  =  50  +  20  -f  (  ) 

24  —  8           6X7           i  of  44  79  =  40  +  25  +  (  ) 

48  —  8           9X8          5  of  44  77  =    7  X  10  +  (  ) 

64  —  8          8X7           |of80  .    73  =  50  +  14  + () 

56  —  8          7X7          i  of  80  78  =    7  X  11  +  (  ) 


NUMBERS    TO    EIGHTY. 


147 


TRIANGLE 


SQUARE 


RECTANGLE 


HEXAGON 


207.  If  each  side  of  the  triangle  is  an  inch  long,  what 
is  the  distance  around  the  triangle?  (The  distance  around 
it  is  called  the  perimeter.) 

How  many  sides  make  the  perimeter  of  the  square? 

What  is  the  perimeter  of  a  square  inch? 

A  table  is  2  feet  square.     Tho  perimeter  is feet. 

If  the  rectangle  is  1  inch  long  and  1  inch  wide,  its 
perimeter  is  -  -  inches. 

How  many  sides  has  the  hexagon?  If  each  side  is  half 

an  inch  long,  the  perimeter  is  -  -  half  inches,  or  

inches. 

A  rectangle  is  3  feet  long  and  2  feet  wide.  What  is 
the  perimeter? 

The  perimeter  of  a  square  is  4  feet.  What  is  the  length 
of  a  side?  What  is  the  figure  called? 

The  perimeter  of  a  triangle  is  15  feet.  One  side  is  8 
inches,  another  is  5  inches.  How  long  is  the  third  side? 

Find  the  perimeter  of  this  room.     Of  this  table. 

Find  the  perimeter  of  a  room  16  feet  long  and  16  feet 
wide. 


208.     In  8  dimes  there  are 


cents. 


I  gave  50^  for  a  book  and  22^  for  a  slate.  How  much 
did  I  give  for  both  ? 

^ Tattie  had  8  climes.  She  gave  5  cents  for  candy,  and 
then  had cents  left. 


148  SCHOOL    AKITHMETIC. 

A  bushel  of  wheat  weighs  60  pounds.  A  bushel  and  a 
peck  weigh pounds. 

How  many  gallons  must  be  added  to  65  gallons  to  make 
78  gallons? 

If  I  have  70  cents,  to  how  many  boys  can  I  give  a  dime 
each? 

Uncle  Henry  is  50  years  old.  How  old  will  he  be  in  24 
years  ? 

The  perimeter  of  a  square  is  12  inches.  Draw  the 
square  and  show  how  many  square  inches  it  contains. 

If  you  had  65  cents  and  each  of  5  boys  gave  you  2 
cents,  how  many  cents  would  you  have? 

Wilbur  earns  53  cents  in  a  day  and  Oscar  44  cents. 
How  much  more  does  Wilbur  earn  than  Oscar  in  8  days? 

Numbers  to   One  Hundred. 

209.  Draw  a  square  9  inches  on  a  side.  Mark  it  off 
into  square  inches. 

How  many  squares  inches  are  there?  How  many  in  1 
row?  How  many  rows? 

9X9  square  inches  =  -  squares  inches. 

81  square  inches  contains  9  square  inches  -       -  times. 

10  X  9  sq.  in.  =  -  sq.  in.       9  X  10  = 

90  -^10  ==         90  -^  9  =  TV  of  90  = 

Make  7  rows  of  12  dots  each,  and  tell  how  many  seven 
12's  are.  How  many  are  twelve  7's? 

How  many  12's  make  84?    How  many  7's? 

Add  by  7's  to  84.  By  8's  to  96.  By  9's  to  99.  By 
10's  to  100. 


NUMBERS  TO  ONE  HUNDRED. 


149 


Write  a  number  which  has  9  in  the  ones'  place.  Can 
you  write  a  number  which  has  ten  in  the  ones'  place  ? 

What  is  the  smallest  number  that  is  written  with  two 
figures  ? 

What  is  the  largest  number  that  can  be  expressed  by 
two  figures? 


210. 

Complete  and  memorize: 

1 

nine  =  9 

1 

X 

9  =  9 

9 

X 

1 

= 

2 

nines  = 

2 

X 

9  = 

9 

X 

2 

= 

3 

nines  = 

3 

X 

9  = 

9 

X 

3 

= 

4 

nines  = 

4 

X 

9  = 

9 

X 

4 

= 

5 

nines  = 

5 

X 

9  = 

9 

X 

5 

= 

6 

nines  = 

6 

X 

9  = 

9 

X 

6 

= 

7 

nines  = 

7 

X 

9  = 

9 

X 

7 

= 

8 

nines  = 

8 

X 

9  = 

9 

X 

8 

== 

9 

nines  = 

9 

X 

9  = 

9 

X 

9 

= 

10 

nines  = 

10 

X 

9  = 

9 

X 

10 

= 

11 

nines  = 

11 

X 

9  = 

9 

x 

11 

— 

Multiply  10  by  3,  7,  5,  4,  8,  6,  9,  10. 
How  many  10's  in  50,  30,  70,  90,  60,  100? 
How  many  9's  in  36,  45,  63,  72,  90,  81? 
How  many  8's  in  40,  56,   64,  80,  72,  88,  96? 


211.      Find 

the  value  of: 

90- 

-9 

80- 

-10 

77- 

-  7 

72- 

-    9 

36- 

-9 

60- 

-10 

63- 

-7 

64- 

-    8 

63- 

-9 

30- 

-10 

84- 

-7 

56- 

-    7 

45- 

-9 

90- 

-10 

66  — 

-6 

54- 

-    6 

54- 

-9 

88- 

-11 

72- 

-6 

49- 

-    7 

72- 

-9 

99- 

-11 

88- 

-8 

42- 

-    6 

81- 

-9 

84- 

-12 

96- 

-8 

60- 

-12 

99- 

-9 

96- 

-12 

72- 

-8 

72- 

-12 

150  SCHOOL    ARITHMETIC. 

212.      How  many  10-cent  dishes  can  I  buy  for  a  dollar? 
A  bath  room  is  9  feet  square.     It  contains  -      -  square 
feet. 

Mr.  Hall  has  12  bushels  of  turnips.  To  how  many 
persons  can  he  sell  1  peck  each? 

A  milkman  has  9  gal.  1  qt.  of  milk.  He  can  sell  1  qt. 
to  each  of  -  customers. 

What  are  7  dozen  eggs  worth  at  a  cent  apiece? 

How  many  days  are  there  in  11  weeks? 

Twelve  men  paid  2  dollars  apiece  to  hire  a  sail  boat.  How 
much  did  they  all  pay? 

If  a  boy's  suit  costs  9  dollars,  how  much  will  10  such 
suits  cost? 

A  man  paid  81  dollars  for  a  horse  and  -g  as  much  for 
a  saddle.  How  much  did  the  saddle  cost  him? 

If  the  whole  of  anything  costs  81  cents,  how  much 
does  -f  of  it  cost  1 

At  his  last  birthday  Edward  had  lived  96  months.  How 
many  years  old  was  he? 

Add  the  days  in  the  month  in  which  Thanksgiving  comes 
to  those  in  the  month  after  and  the  month  before. 

Slate  Work. 

213.  How  many  dollars  are  $32  and  $32  and  $32,  or 
3  X  $32? 


Three  times  2  ones  are  6  ones.    Write  the  6 

$96 


in  ones'  place.     Three  times  3  tens  are  9  tens. 
Where  do  we  write  the  9  ? 


SLATE    WOKK. 


151 


Multiply: 
42   '      23 

2  3 


34 

2 


31 
3 


44 

2 


21 
3 


32 

2 


The  perimeter  of  a  square  room  is  48  feet.     What  is  the 
length  of  each  side? 

'  feet  Each  side  is  I  of  the  perimeter.     J  of  4  tens  is  1 

12  feet  ^en>  an<^  *  °^  ^  °nes  is  2  ones.     ^  of  48  feet  is  12  feet. 

Find  1  of  $84,  J  of  66  yd.,  1  of  46  gal.,  i  of  96^. 
How  many  3's  in  36? 
3  )  36          3  )  36 
12 


10 


12 

Find  how  many: 
2's  in  28. 
3*s  in  96. 

Divide : 

2)  68  3)  69 


In  3  tens  there  are  10  threes.  In  6  ones 
there  are  2  threes.  10  threes  and  2  threes 
are  12  threes. 


3's  in  63. 

4's  in  88. 


2)  86 


3)96 


2)  64 
9)99 


4)44 

4)88 


4's  in  48. 
2's  in  84. 


5)  55        7)  77 


6)  66 


8)  88 


214.  This  is  a  cube.  How 
many  sides,  or  faces,  has  it  \ 

What  is  the  length  of  each 
face  \  The  width  \ 

Are  the  faces  all  of  the  same 
size  \  Each  face  is  a inch. 

A  cube  that  is  an  inch  long., 
an  inch  wide,  and  an  inch  thick 
is  called  a  cubic  inch  (cu.  in.). 


SCHOOL    ARITHMETIC. 

Find  a  block  that  is  a  cubic  inch. 

Place  4  such  blocks  in  a  row.  How  many  cubic  inches 
in  the  row? 

Place  4  more  cubes  beside  these.  How  many  cubic 
inches  in  the  2  rows? 

Place  8  more  cubes  on  top  of  these.  How  S /' S  S^"*^ 
many  cubic  inches  in  each  layer?  How  [\  I  I  P^ 
many  in  both  layers? 

215.  With  one-inch  cubes  build  a  cube  2  inches  on 
each  side. 

How  many  layers  are  there?  How  many  rows  in  each 
layer?  How  many  one-inch  cubes  in  each  row? 

How  many  cubes  in  both  rows?     In  both  layers? 

How  many  cubic  inches  in  the  cube  you  have  built? 

A  cube  2  inches  on  a  side  is  a  two-inch  cube.  It  con- 
tains   cubic  inches. 

A  one-inch  cube  is  what  part  of  a  two-inch  cube? 

A  two-inch  cube  is  how  many  times  a  one-inch  cube  ? 

Point  out  |  of  a  two-inch  cube.     \  of  it. 

How  many  fourths  of  the  two-inch  cube  equal  \  of  it? 

How  many  eighths  of  the  two-inch  cube  equal  i  of  it? 

One-fourth  is  what  part  of  one-half? 

One-half  of  one-half  is  one . 

216.  Build    a    cube    having  3  layers,  3  rows  in  each 
layer,  and  3  one-inch  cubes  in  each  row. 

This  cube  is  -  -  inches  on  each  side,  and  contains 
cubic  inches. 

It  is  a  three-inch  cube  and  contains one-inch  cubes. 

Nine  one-inch  cubes  are  what  part  of  the  3-inch  cube? 
18  one-inch  cubes  are  what  part? 


REVIEW    AND    DRILL    WORK. 


153 


How  many  square  inches  in  each  face  of  the  3-inch  cube? 
In  3  faces?  In  all  the  faces? 

How  many  inch  cubes  will  be  needed  to  make  a  pile  6 
in.  long,  3  in.  wide,  and  2  in.  high? 


Review  and  Drill  Work. 


217, 


1. 

2. 
3. 

4. 
5. 
6. 

7. 
8. 

a 

4 
7 
5 
6 
8 
4 
6 
9 

b 

8 
4 
'  6 
5 
4 
6 
7 
5 

c 

7 
8 
7 
4 
5 
8 
9 
6 

d 

4 
6 

8 
3 
6 

7 
4 

8 

e 

9 

2 

7 
5 
4 
6 

8 

f-r 
< 

f 

6 
5 
4 

7 
5 
4 

7 
6 

g 

8 
2 
6 
5 
7 
3 
8 
5 

h 
5 

7 
4 
6 
3 
8 
5 
4 

i 
4 

8 
3 
8 
4 

7 
6 
5 

i 

7 
4 
5 
7 
3 
9 
2 
6 

k 

6 
5 

7 
5 
8 
5 

8 

7 

1 
8 
3 
8 
4 
9 
4 
7 
8 

m 
9 

2 
9 
2 
8 
6 
5 
6 

n 

6 

/— 
i 

6 
4 

8 
7 
6 
8 

8 


Add  the  numbers  in  each  line. 

Add  the  numbers  in  each  column. 

Multiply  the  numbers  in  each  column  by  3;  4?  5?  6,  7, 

.  9- 

Multiply  the  numbers  in  column  h  by  8,  and  those  in 
column  m  by  7,  and  find  the  sums  and  differences  of  each 
two  corresponding  results. 

218.      Complete: 


-2  = 

49- 

-7  = 

42- 

-6  = 

63  -f-    9 

—  4  = 

48- 

-8  = 

27- 

-3  = 

54^-9 

—  5  = 

84- 

-7  = 

28- 

-4  = 

81-*-   9 

-3=±= 

18- 

-3  = 

40- 

-4  = 

56  -f-    7 

-9  = 

33- 

-3  = 

63- 

-7-= 

84-^12 

-3  = 

64- 

-8  = 

72- 

o  

45  -f-    3 

154  SCHOOL    ARITHMETIC. 

219.  How  many  — 

yards  in  30  ft.?  dimes  in  90^? 

pecks  in  24  qt.?  gallons  in  28  qt.? 

feet  in  96  in.?  dollars  in  30  dimes? 

bushels  in  32  pk.?  pints  in  44  qt.? 

weeks  in  49  days?  yards  in  27  feet? 

ounces  in  2  lb.?  half -pecks  in  2  bu.? 

quarts  in  48  pt. ?  shoes  in  30  pairs? 

dimes  in  33^?  tens  in  35  ones? 

220.  Find  the  cost  of: 

9  lb.  of  sugar  at  6^  a  pound. 

4  quires  of  paper  at  10^  a  quire. 

8  qt.  of  peanuts  at  6^  a  quart. 

9  yd.  of  silk  at  $4  a  yard. 

1  dozen  papers  at  3#  each. 

2  bu.  of  salt  at  4^  a  quarter-peck. 

221.  Find  the  perimeter  and  area  of: 

A  rectangle,  7  inches  by  4  inches. 
A  rectangle,  8  inches  by  3  inches. 
A  rectangle,  9  inches  by  4  inches. 
A  rectangle,  12  inches  by  5  inches. 
A  square,  measuring  3  inches  on  a  side. 
A  square,  measuring  4  inches  on  a  side. 

222.  Take  inch  cubes  and  build  a  pile  4  blocks  long, 
3  blocks  wide,  and    2    blocks    high.     Then    fill    out    the 
following: 


REVIEW    AND    DRILL  WORK.  155 

Length  of  one  side  =  -      -  inches. 

Height  of  one  side  =  -  -  inches. 

Area  of  one  side       =  —  sq.   in. 

Width  of  one  end     =  —  —  inches. 

Area  of  one  end      =  —  —  sq.  in. 

Area  of  the  top  —  sq.  in. 

Area  of  all  six  sides  =  —  —  sq.  in. 

Xumber  of  cubes  in  the  pile  =  —  — . 


223.     Draw  a  square  that  contains  49  square  inches. 

Draw  a  rectangle  that  contains  30  square  inches. 

James  is  10  years  old.  His  age  is  i  of  his  father's  age. 
How  old  is  his  father? 

When  oil  is  worth  20  cents  a  gallon,  how  much  can  be 
bought  for  5  cents? 

If  you  take  2  quarts  of  milk  a  day  at  6^  a  quart,  how 
much  will  your  milk  cost  you  for  a  week? 

How  much  must  you  pay  if  you  buy  7  yards  of  cloth 
at  9^  a  yard? 

If  there  are  4  sq.  in.  in  the  face  of  a  cube,  how  many 
square  inches  are  there  in  all  the  faces? 

24  sheets  of  paper  make,  a  quire.  Find  how  many 
sheets  there  are  in  a  quire  and  a  half  of  a  quire. 

Xaine  all  the  months  of  the  year  that  have  31  days. 

From  1  o'clock  in  the  morning  until  nine  o'clock  in 
the  evening  is  how  many  hours? 

If  your  oil  can  holds  2  gal.  and  your  lamp  holds  2 
quarts,  how  many  times  can  you  fill  your  lamp  from  your 
can? 

Show  by  lines  that  -J-,  |,  and  -|  are  the  same  in  value. 


156  SCHOOL    ARITHMETIC. 

Hundreds. 


one  ten  hundred 

224.  How  many  ones  make   1   ten?     How  many  tens 
make  1  hundred  1 

Show  me  10  tens  with  splints.  Put  a  band  around  them. 
How  many  ones  are  in  the  bundle? 

Make  another  bundle  of  100.  How  many  ones  are  in 
both  bundles?  How  many  hundreds? 

One  hundred  and  4  hundreds  are  -      -  hundreds. 

Four  hundreds  and   5  hundreds  are  -       -  hundreds. 

How  many  cents  make  1  clime  ?  How  many  dimes  make 
a  dollar?  How  many  cents  make  a  dollar? 

One  hundred  cents  make  a,  dollar. 

How  many  cents  in  5  dollars?     In  8  dollars? 

In  what  place,  counting  from  the  right,  do  wo  write  the 
figure  for  the  number  of  tens? 

In  what  place  do  you  think  we  should  write  the  hundreds 
of  a  number? 

225.  Supply  the  figures  needed: 

One  hundred  is  written  thus  —  100. 
Two  hundred  is  written  thus  —  200. 
Three  hundred  is  written  thus  — 


HUNDREDS.  157 

Four  hundred  is  written  thus  — 
Five  hundred  is  written  thus  — 
Six  hundred  is  written  thus  — 
Seven  hundred  is  written  thus  — 
Eight  hundred  is  written  thus  — 
Nine  hundred  is  written  thus  — 
Ten  hundred  is  written  thus  —  1000.  One  thousand. 

226.  Copy  and  complete: 

10  tens  make     100.  60  tens  make  -  — . 

20  tens  make  -     — .  80  tens  make . 

30  tens  make  -    — .  70  tens  make  -   — . 

40  tens  make  -     — .  90  tens  make  -  — . 

50  tens  make  -     — .  100  tens  make  -  — . 

100  ~-  10  tens.  600  =  -  tens. 

500  =  -  -  tens.  800  =  -  tens. 

300  =  -  -  tens.  700  =  -  tens. 

400  =  -  tens.  900  =  -  tens. 

200  =  -  tens.  1000  =  -  tens. 

227.  Add: 

$5  50o</  $4 

3  3000  5 


4  hundreds 
3   " 

40  tens 
30  " 

200  sheep 
400   " 
300  " 

400  ones 
300  " 

100  miles 
300   " 
500  " 

$100 
600 
200 

158 


SCHOOL    ARITHMETIC. 


228.     Subtract: 
$6  600^ 

$2  200# 

7  hundreds 
3        " 


60  dimes 

20      " 


70  tens 
30     " 


700  ones 
300     « 


900 
200 


700 
400 


600 
100 


800 
500 


900 
TOO 


229.    Copy  and  complete: 


100  +  300  = 

500  +  100  = 

300  +  600 

200  +  400  - 

400  +  300  - 

500  +  400 

400  +  200  = 

700  +  200  - 

100  +  800 

600  +  300  = 

100  +  GOO  = 

300  +  500 

300  +  200  = 

200  +  500  = 

400  +  600 

Hundreds  and  Tens. 


t 

0 

h 

t 

o 

h         t 

\ 

0 

1 

0 

1 

0 

0 

i  |  t 

0 

230.  In  writing  ten  in  figures,  why  do  we  put  0  in  ones' 
place  ? 

In  writing  one  hundred  in  figures  we  put  0  in  two 
places.  Why? 

How  many  ones  can  be  written  with  one  figure?  How 
many  tens?  How  many  hundreds? 

How  do  you  write  1  ten  and  1  one  in  figures? 

How  do  you  think  1  hundred  and  1  ten  should  be 
written? 


HUNDREDS    AND   TENS.  159 

One  hundred  and  one  ten  is  written  thus  —  110. 
One  hundred  and  two  tens  is  written  thus  —  120. 
One  hundred  and  three  tens  is  written  thus  —  130. 
One  hundred  and   ten   tens   is   written   thus  —  200. 
Two  hundreds  and  one   ten  is  written  thus  —  210. 
Three  hundreds  and  five  tens  is  written  thus  —  350. 

231.  Copy  and  complete: 

1  hundred  +  1   ten   -- =  110.  1   hundred    +9  tens  — 

1  hundred  +  3   tens  =  2  hundreds  +  3  tens  = 

1  hundred  +  7   tens  =  2  hundreds  +  6  tens  = 

1  hundred  +  5   tens  =  2  hundreds  +  5   tens  = 

1  hundred  +  4  tens  =  3  hundreds  +  1  ten   = 

1  hundred  +  8  tens  =  3  hundreds  +  4  tens  = 
100  +  80  =  300  +  40  = 

One  hundred  and  two  tens,  or  120,  is  read  one  hundred 
twenty. 

How  then  should  140  be  read?  250?  230?  360? 
510?  74G? 

Count  by  10's  from  100  to  300.  From  300  to  500. 
From  500  to  1000. 

How  many  hundreds  and  how  many  tens  in  240?  In 
360?  In  580? 

232.  Copy  and  complete: 

260  =  2  h  +  6  t  430  =  4  h  +  3  t 

320  =  680  = 

410  =  740  = 

630  ==  590  = 

540  =  860  = 

.  720  =  770  = 

810=  990  = 

950=  870  = 


160 


SCHOOL    ARITHMETIC. 


What  number  contains  4  hundreds  and  3  tens?  Two 
hundreds  and  5  tens? 

Count  by  10's  from  300  to  600,  and  write  the  numbers 
as  you  count. 

Show  with  sticks  what  is  expressed  by  each  figure  in 
140.  In  250. 

How  many  tens  in  100?  In  200?  In  500?  In  250? 
In  120?  In  210? 


233.  Read: 

150,      180,      210, 
280,      470,      390, 

234.  Write  in  figures: 
One  hundred  forty. 
One  hundred  sixty. 
Two  hundred  thirty. 


320, 

760, 


430,      540, 
920,       650, 


360, 

870. 


Four  hundred  fifty. 

Six  hundred  ten. 

Eight  hundred  seventy. 
Two  hundred  twenty.      Seven  hundred  eighty. 
Three  hundred  eighty.     Nine  hundred  forty. 
Five  hundred  ninety.        Nine  hundred  ninety. 

Hundreds,  Tens,  and  Ones. 


h 

t 

0 

1 

0 

1 

k 

t 

0 

1 

2 

4 

235.  In  writing  1  hundred  and  1  one,  or  1  more  than 
100,  what  do  we  write  in  the  ones'  place?  In  the  tens' 
place  ? 

In  writing  124  what  do  we  write  in  ones'  place?  In 
tens'  place? 

Count  from  100  to  200,  and  write  the  numbers  as  you 
count. 


HUNDREDS 


161 


Numbers  from  100  to  1000  are  written  as  follows: 
One  hundred,  100. 

One  hundred  one,  101. 

One  hundred  two,  102. 


Two  hundred  one,  201. 

Two  hundred  twelve,  212. 

Two  hundred  forty-six,  246. 

Nine  hundred  ninety-nine,     999. 
One  thousand,  1000. 

How  many  hundreds  in  132?  How  many  tens?  How 
many  ones? 

How  many  hundreds,  tens,  and  ones  in  245?  In  328? 
In  612? 


236.  Eead: 

25 

42 

30 

90 

81 

325 

542 

130 

290 

781 

16 

23 

17 

84 

10 

216 

423 

217 

484 

810 

37 

66 

36 

3 

98 

437 

666 

336 

303 

898 

237.      Write  in  figures: 

Forty-one. 

Two  hundred  forty-one. 

Sixty-four. 

Six  hundred  sixty-four. 

Eighty-nine. 

Four  hundred  eighty-nine. 


Eleven. 

Five  hundred  eleven. 

Thirty-six. 

Three  hundred  thirty-six. 

Ninety. 

Nine  hundred  ninetv. 


100- 

h30H 

h  2  =  132 

100- 

h20H 

r  5  = 

200- 

I-10H 

h  6"  = 

200- 

h40H 

h7  = 

500- 

h30H 

r  8  = 

300- 

h60H 

h4  = 

400- 

h40- 

h4  = 

700- 

h80- 

hV  = 

600- 

1-20H 

hO  = 

800- 

h  OH 

h8  -  = 

162  SCHOOL    ARITHMETIC. 

238.     Copy  and  complete: 
Hundreds    tens    ones 

1  +  3  +  2  =  =  132. 
1+2 

2  -f 

2  -f 

5  -i 
4     -+ 

6  -i 

8  -i 

3  H- 

9  -I 

Dollars  dimes  cents  cerits  Dollars  dimes  cents  cents 

1  +     5  +  5  =  155  2     +  3  +  1  =  =  231 

1+4  +  2=  3+5  +  4  = 

3+2  +  8=  5+7  +  5  = 

4+6  +  0=  6+9  +  0  = 

2+0  +  5=  '       7+0  +  8  = 

5+0  +  0=  4+4  +  4  = 

In  325  cents,  the  5  represents  cents,  the  2  represents 
dimes,  and  the  3  represents  dollars,  or  hundreds  of  cents. 

What  does  each  figure  in  427  cents  represent? 

In  555  cents,  which  five  represents  the  greatest  value? 
Which  represents  the  least  value? 

Which  5  represents  50  cents?  Which  represents  5 
cents? 

Then  the  middle  5  represents  10  times  as  much  as 
which  5? 

Which  5  represents  10  times  as  much  as  the  middle  5? 


ADDITION    AND    SUBTRACTION.  163 

Show  how  many  dollars,  dimes,  and  cents  there  are  in 
215  cents. 

How  many  hundreds,  tens,  and  ones  are  there  in  348? 
In  592?    In  402? 

How  many  figures  are  needed  to  write  hundreds?    How 
many  to  write  hundreds,  tens,  and  ones? 

Addition  and  Subtraction. 
239.   Add: 


1 

2 

3 

4 

5 

6 

24 

92 

57 

68 

90 

27 

87 

87 

86 

94 

76 

46 

68 

69 

75 

76 

84 

84 

96 

34 

68 

45 

59 

68 

7 

8 

9 

10 

11 

12 

49 

94 

84 

65 

7 

92 

74 

87 

76 

29 

84 

37 

98 

39 

18 

84 

68 

48 

65 

65 

54 

76 

42 

51 

83 

56 

63 

17 

79 

76 

13 

14 

15 

16 

17 

18 

28 

81 

63 

37 

97 

28 

46 

63 

81 

96 

2 

84 

92 

9 

5 

42 

85 

61 

74 

27 

37 

88 

46 

79 

19 

45 

19 

4 

58 

46 

37  76  46  73  39  3T 


164  SCHOOL    ARITHMETIC. 


19 

20 

21 

22 

23 

24 

76 

64 

95 

76 

12 

74 

32 

93 

26 

90 

37 

29 

23 

89 

7 

39 

45 

83 

67 

46 

80 

68 

79 

^8 

51 

57 

78 

85 

28 

45 

24 

54 

38 

42 

55 

45 

36 

36 

47 

36 

84 

83 

45 

79 

62 

7 

83 

37 

240.     Subtract  286  from  753. 

753  We  cannot  take  6  ones  from  3  ones,  so  we  add  10  ones  to 

286          the  3  ones,  and  take  6  from  13.     Where  do  we  get  the  10 

ones  ?    How  many  tens  are  left  ? 
467  Can  we  take  8  tens  from  4  tens?    Then  we  must  add  10 

tens  to  the  4  tens,  and  take  8  from  14.  Where  do  we  get 
the  10  tens?  How  many  hundreds  are  left?  2  hundreds  from  6 
hundreds  leaves  4  hundreds. 

Add  467  and  286.     If  the  sum  is  753,  the  subtraction 
is  correct. 

Subtract  and  prove: 

123  456 

714     635     582  .   745     827     610 
362     271     175     476     572     247 


7 

8 

9 

10 

11 

12 

921 

824 

732 

.672 

523 

624 

473 

547 

435 

48 

149 

258 

ADDITION    AND    SUBTRACTION. 


165 


13 

14 

15 

16 

17 

18 

362 

521 

607 

300 

815 

935 

57 

412 

278 

27 

726 

786 

19 

20 

21 

22 

23 

24 

872 

360 

706 

982 

617 

308 

375 

97 

418 

387 

419 

199 

241.     Copy  and 

1.  475+65=  ' 

2.  582+78= 

3.  368+53= 

4.  729+94= 

5.  647+85= 

6.  768+74= 

7.  526+59= 

8.  395+67= 


complete : 

9.  248+376: 

10.  426+187: 

11.  519+183: 

12.  372+439: 

13.  582+276: 

14.  766+180: 

15.  647+273: 

16.  504+396; 


17.  527—348-= 

18.  716—297= 

19.  432—186= 

20.  666—378  = 

21.  500—275= 

22.  807—508= 

23.  431—276= 

24.  760—498= 


242.     1.     How  much  will  a  span  of  horses  cost  if  one 
horse  costs  85  dollars  and  the  other  105  dollars? 

2.  In  a  box  were  85  oranges.     If  the  box  would  hold 
125,  how  many  more  oranges  would  it  take  to  fill  it? 

3.  A  boy  shoots  one  arrow  97  yards  up  the  road,  and 
another  65  yards  down  the  road.     How  many  yards  apart 
are  the  two  arrows? 

4.  Mr.   Thomas  paid  $625  for  a  lot,  and  sold  it  for 
$900.     How  much  did  he  make? 

5.  Three  men  have  $980.     One    has    $145,  another 
has  $321.     How  much  has  the  third  man? 

6.  I  can  buy  a  candy  store  for  $825,  but  I  have  only 

How  much  more  do  I  need? 


166  SCHOOL    ARITHMETIC. 

7.  Mr.  Johnson  raised  345  bushels  of  corn,  475  bushels 
of    oats,    and    128    bushels  of    wheat.     He    raised  - 
bushels  in  all. 

8.  One  week  a  milkman  sold  284  qt.  of  milk,  the  next 
week  296  qt.,  the  next  week  318   qt.,  and  the, next  week 
72  qt.      In  the  four  weeks  he  sold quarts. 

9.  Martin  weighs   128   lb.,    Frank   96   lb.,   Jack   116 
lb.,  Rob  87  lb.,  and  Will  131  lb.     How  much  do  all  five 
boys  weigh? 

10.  A  storekeeper  had  970  bushels  of  potatoes.     One 
week  he  sold  265  bu.,  and  the  next  week  325  bu.     How 
many  bushels  had  he  left? 

11.  On  Monday  morning  a  freight  train  started  to  run 
962  miles.     The  first  day  it  ran  316  miles,  the  second  day 
it  ran  373  miles.    It  still  had  -     -  miles  to  run. 

12.  September,  April,  June,  and  November  each  has 
30  days.    February  has  28  days  except  in  leap  years,  when 
it  has  29.     All  other  months  have  each  31  days.     How 
many  days  in  all  the  months,  or  in  a  year? 

Multiplication  and  Division. 
243.     Multiply: 

243  321  434  233  212 

23234 


211  322  423  534  412 

54324 


Take  46  splints,  4  tens  and  6  ones.     How  many  would 
you  have  if  you  had  4  times  as  many? 


MULTIPLICATION    AND    DIVISION.  167 

Four  times  6  splints  =  24  splints.  How  many  tens  and 
how  many  ones  in  the  24  splints. 

Four  times  4  tens  =  16  tens.  16  tens  and  2  tens  are 
18  tens.  You  would  have  18  tens  and  4  ones,  or  184 
splints. 

46  =     4  t  +  6  o 
4  4 


184  =  16*  +  24o  =  18*  +4<? 


Multiply  246  by  4. 


246'  246  =  2  A  +  ±t  +  So 

246  4  4 


984  =  9  h  +  8  *  +  4  -9 

984 

We  can  find  the  result  by  adding,  but  there  is  a  snorter  process. 
4  times  6  ones  =  24  ones.  We  write  the  4  ones  under  the  6  ones, 
and  "carry"  the  2  tens  to  add  with  the  tens.  4  times  4  tens  =  16 
tens.  The  2  ones  we  had  to  carry  make  18  tens,  or  1  hundred  and  8 
tens.  We  write  the  8  tens  under  the  4  tens,  and  carry  the  1  hundred. 
4  times  2  hundreds  are  8  hundreds  and  the  1  hundred  makes  9  hun- 
dreds. Where  is  the  9  hundreds  written  ? 

MI 

Multiply  : 

123456 

45.  36  25  35  143  125 

345345 


7 

8 

9 

10 

11 

12 

216 

117 

228 

170 

280 

181 

4 

5 

3 

2 

3 

4 

168  SCHOOL    ARITHMETIC. 


13 

14 

15 

16 

17 

18 

242 

5 

162 

6 

136 
6 

172 
5 

196 
4 

23 

167 
5 

19 

20 

21 

22 

24 

152 
6 

138 
7 

126 

8 

119 

7 

137 

7 

128 

7 

25 

26 

27 

28 

29 

30 

108 

8 

107 

9 

117 

8 

163 

6 

69 

8 

76 
9 

31 

32 

33 

34 

35 

36 

35 
12 

24 
12 

32 
11 

51 
11 

62 
12 

44 
12 

244.     Examine  carefully: 

5  multiplied  by  10  -      50.  10  X    7  =    70. 

8  multiplied  by  10  =80.  10  X  2  -  20. 

10  multiplied  by  10  ==  100.  10  X  9  =  90. 

12  multiplied  by  10  =  120.  10  X  20  =  200. 

15  multiplied  by  10  ==  150.  10  X  50  =  500. 

Annexing  0  to  a  number  multiplies  it  by  10. 

Announce  results  at  sight: 

10  X     7  10  X  25  10  X  60 

10  X  11  10  X  30  10  X  66 

10X14  10X36  10X70 

10  X  18  10  X  40  10  X  75 

10  X  20  10  X  48  10  X  87 

10  X  24  10  X  50  10  X  98 


MULTIPLICATION    AND    DIVISION. 

245.    Divide: 


169 


(a) 
00 

to 
(*) 
w 

(f) 
(*) 

(h) 

(i) 

2)486 

2)  682 

2)248 

3)  636 

6)660 

3)369 

4)  844 

4)480 

5)  555 

8)888 

2)100 

2)128 

3)  126 

3)  150 

3)  189 

4)  168 

4)204 

4)284 

4)  320 

4)368 

5)  105 

5)  150 

5)  200 

5)355 

5)  550 

6)126 

6)240 

6)366 

6)420 

6)  546 

7)  140 

'  7)217 

7)280 

7)357 

7)  630 

8)  160 

8)  248 

8)400 

8)  560 

8)728 

9)  639 

9)  720 

9)  810 

9)  909 

9)  990 

246.     Examine  carefully: 

50^-10=      5 

30.-f-10=      3 

80-^10=-    8 

100 -f- 10 -=10 


120 -f- 10  =  12 

150 -r- 10  =  15 
200-^-10  =  20 
250-^10  =  25 


Annexing  a  cipher  to  a  number  multiplies  that  number 
by  10.    Show  that  cutting  oft'  zero  divides  a  number  by  10. 


247.      Name  results  at  sight: 


50  —  10 

70  —  10 

40  —  10 

60  —  10 

110  —  10 

130  —  10 


140  —  10 
180  —  10 
200  —  10 
270  —  10 
300  —  10 
320  —  10 


400 
460 
510 
680 
790 
940 


10 
10 
10 
10 
10 
10 


170  SCHOOL   ARITHMETIC. 

248.  To  find  i  of  75  splints,  take  7  tens  and  5  ones,  and 
divide  them  into  5  equal  piles.  Each  pile  will  contain 
i  of  the  75.  How  shall  we  proceed  to  make  the  5  piles? 

5)  75  $  of  7  tens  =  1  ten  for  each  pile,  but  there  are  2  tens 
~~T           left  out.     2  tens  and  5  ones  =  25  ones.    £  Of  25  ones  ==  5 

ones  for  each  pile.     Hence  each  pile  has  1  ten  -f  5  ones, 
or  15  splints. 

1.  Divide  738  by  6. 

6)  738  7  hundreds  -=-6  —  1  hundred,  and  1  hundred  remain- 

~l¥s      ing* 

The  remainder  1  hundred  equals  10  tens,  which  with 
the  3  tens  makes  13  tens. 

13  tens  -4-6  =  2  tens,  and  1  ten  remaining.     1  ten  and  8  ones  =  18 
ones.     18  ones  -=-6  =  3  ones. 
Explain  this  division  by  using  splints. 

2.  Divide  375  by  5. 

Since  3  does  not  contain  5,  we  take  the  3  hundreds  or 
5)  375         30  tens  and  put  them  with  the  7  tens,  making  37  tens. 
— —         Then  37  tens  -=-5  =  7  tens,  and  2  tens  remaining. 

*  ^  The  2  tens  or  20  ones  put  with  the  5  ones  make  25  ones. 

25  ones  -5-5  =  5  ones. 


Divide  : 

3 

4 

5 

6 

7 

8 

2)236 

2)112 

2)154 

2)  178 

2)192 

2)  254 

9 

10 

11 

12 

13 

14 

2)  176 

2)452 

2)  634 

2)  816 

2)412 

2)630 

15 

16 

17 

18 

19 

20 

3)168 

3)195 

3)351 

3)  642 

3)975 

3)678 

21 

22 

23 

24 

25 

26 

3)426        3)753        3)826        3)525        3)432        3)528 


MULTIPLICATION   AND   DIVISION.  171 


27 

4)452 

28 

4)896 

29 

4)568 

30 

4)604 

31 

4)720 

32 

4)  956 

33 

5)625 

34 

5)675 

35 

5)720 

36 

5)835 

37 

5)960 

38 

5)  985 

39 

6)  132 

45 

7)154 

40 

6)198 

41 

6)252 

42 

6)  618 

48 
7)714 

43 

6)714 

44 

6)804 

46 

7)112 

47 

7)105 

49 

7)798 

50 

7)861 

51 

8)176 

52 

8)104 

53 

8)  256' 

54 

8)736 

55 

8)984 

56 

8)  992 

57 

9)117 

58 

9)198 

59 

9)288 

60 

9)657 

61 

9)765 

62 

9)  846 

249.    1.     What  number  multiplied  by  7  is  equal  to  84? 

2.  What  number  divided  by  6  is  equal  to  72?  To  720? 

3.  Find  one  of  the  4  equal  parts  of  96.    Of  240. 

4.  Of  what  number  is  25  one-fourth?     One-eighth? 

5.  Fifty  is  ^  of  what  number?     y^  of  what  "number? 

6.  If  24  is  f  of  some  number,  what  is  ^  of  the  number? 

7.  If  $20  is  §  of  my  money,  how  much  money  have  I? 

8.  A  train  runs  315  miles  in  9  hours.     How  far  does 
it  run  in  1  hour? 

9.  If  3  organs  cost  $180,  how  much  does  one  cost? 

10.  If  1  organ  costs  $60,  how  much  will  10  cost? 

11.  At  the  rate  of  2  for  5  cents,  what  will  a  dozen 
lemons  cost?     (12  =  how  many  2's?) 

12.  What  will  10  books  cost  if  2  books  cost  $3  \     10  is 
•how  many  times  2?     The  cost  of  10  books  will  be  how 
many  times  $3? 


172 


SCHOOL    ARITHMETIC. 


13.  If  you  read  23  pages  each  day,  how  many  pages 
will  you  read  in  a  week? 

14.  How  many  boxes  will  hold  117  pounds  of  candy, 
if  3  pounds  are  put  in  each  box? 

15.  In  a  year  there  are  365  days.     How  much  more 
than  52  weeks  is  that? 

16.  At  $7  a  barrel,  how  many  barrels  of  flour  can  be 
bought  for  $413? 

17.  A  rectangle  is  81  inches  long  and  7  inches  wide. 
How  many  square  inches  does  it  contain? 

18.  Three    boys    have    43    quarts  of   nuts,  and    they 
gather   32   quarts  more.      If  they  divide    them    equally 
among  themselves,  how  many  quarts  will  each  receive? 

19.  How  many  inch-cubes  can  you  put  into  a  box  that 
measures  in  the  inside  5  inches  long,  4  inches  wide,  and 
3  inches  deep? 

United  States  Money. 


250.    How  many  cents  make  a  dime? 
How  many  dimes  make  a  dollar? 
Then  how  many  cents  make  a  dollar? 

10  cents  make  1  dime. 

10  dimes,  or  10O  cents,  make  1  dollar. 

One  dollar  is  written  $1,  or  $1.00.    The  sign  $  is  called 


UNITED    STATES    MONEY.  173 

the  dollar  mark,  and  is  placed  before  the  figures  express- 
ing dollars.  Four  dollars  and  twenty-five  cents  is  written 
$4.25.  The  dot  after  the  $4  in  $4.25  means  that  the  two 
figures  on  the  right  stand  for  cents,  and  the  figures  on  the 
left  stand  for  dollars.  This  dot  is  called  the  decimal  point. 

251.      Head  the  following: 


$4.75 

$6.20 

$8.10 

$2.05 

$5.05 

$4.50 

$2.84 

$1.90 

$3.60 

$4.40 

$3.25 

$7.15 

$5.35 

$9.01 

$8.16 

Write  the  following: 

Two  dollars  and  fifty  cents.  One  dollar  and  twenty-five 
cents.  One  dollar.  Five  dollars  and  forty  cents.  Eight 
dollars  and  five  cents.  Ten  dollars  and  seventy-five  cents. 
Six  dollars  and  two  cents.  Nine  dollars  and  fifteen  cents. 

252.  When  there  are  no  dimes  or  cents  we  do  not  need 
to  use  the  dot  unless  we  write  ciphers  in  the  place  of  dimes 
and  cents. 

Read  the  following: 

$5  $10  $50  $100  $125  $500 

$1  $25  $75  $110  $206  $640 

$4.00       $2.00         $8.00         $105  $30.00         $75.00 

When  there  are  no  dollars  to  write  we  place  the  dot 
between  the  dimes  and  the  dollar  mark. 

Read  the  following: 

$.25  $.75  $.10  $.01  $.07  $.09 

$.50  $.90  $.05  $.20  $.85  $.99 


174:  SCHOOL    ARITHMETIC. 

Write  in  figures: 

Thirty  dollars.  One  hundred  five  dollars.  Four  hun- 
dred ten  dollars.  Five  hundred  dollars.  Twenty-five  cents. 
Sixty  cents.  Ten  cents.  Five  cents.  Thirty  cents.  One 
cent.  Eighty-eight  cents.  Seven  cents.  Twelve  cents.. 
Five  dollars  and  five  cents. 

253.    Write  as  dollars  and  cents  : 

150^  175^  225^  360$*  105^  310^ 

420^  500^  713^  609^  220#  666^ 


=  $3.25 


Complete  and 

read: 

Dollars 

Dimes 

Cents 

3 

2 

5 

5 

1 

6 

0 

7 

0 

2 

4 

8 

8 

3 

0 

0 

0 

4 

4 

0 

0 

0 

5 

2 

9 

6 

7 

254.    Dollars,  dimes,  and  cents  are  added  just  as  hun- 
dreds, tens,  and  ones  are  added. 

Dol.       Dimes           $  What  is  written  in  the  first 

o                 .                 K   _       too  AK.  column?  In  the  second  ?  In 

^'4t  the  third? 

4                5                8   =      4.58  Are  the  dots  all    in  one 

7                6  .              0   =      7.60  column? 

—  How  do  we  get  14  dollars 

14              6              3  =$14.63  in  the  sum? 


UNITED    STATES    MONEY.  175 

Find  the  sums: 


$12.15 

$16.52 

$21.45 

$60.76 

7.06 

5.01 

8.72 

28.09 

8.29 

7.75 

6.34 

7.84 

4.80 

30.40 

5.80 

3.63 

36.94 

28.89 

10.10 

5.00 

Find  the  differences: 


$84.75 

$70.20 

$37.00 

$64.03 

26.38 

•     8.05 

25.25 

28.85 

Multiply: 

$14.16 

$15.10 

$12.25 

$24.75 

3 

4 

5 

3 

$42.48 

$51.80 

$42.34 

$28.04 

$37.43 

6 

5 

7 

8 

Divide  : 

2)  $48.76 

3)  $48.51 

2)  $75.20 

2)  $25.00 

$24.38 

255.  1.  One  month  Mr.  Gray  paid  $22.50  for  rent, 
$4.80  for  milk,  $26.78  for  groceries,  and  $6.37  for  gas. 
How  much  did  he  pay  for  all  ? 

2.  I  owe  $32.20  for  coal,  If  I  pay  $25  now,  how  much 
shall  I  still  owe  $ 


176  SCHOOL    ARITHMETIC. 

3.  A  man  bought  6  cows  at  $24.75  each.     He  paid 
$ for  all. 

4.  A  dealer  paid  $112.25  for  5  stoves.     What  was  the 
price  of  one? 

5.  A  farmer  paid  $328  for  two  horses.     He  sold  one 
for  $197.50,  and  the  other  for  $187.50.     What  was  his 
profit? 

6.  Find  the  cost  of  10  acres  of  land  at  $85  an  acre. 

* 

7.  Mrs.  Brown  gave  $320  for  10  cows.     How  much 
did  she  pay  for  one  cow? 

8.  How  many  pounds  of  sugar  at  5^  a  pound  can  you 
buy  for  75^? 

9.  If  I  can  buy  2  oranges  for  5^,  how  many  can  I  buy 
for  a  half-dollar? 

Oral  Exercises. 
256.     How  much  money  in : 

a.  1  5-dollar  bill,  3  2-dollar  bills,  1  silver  dollar,  1  half 
dollar,  and  1  quarter? 

b.  1  10-dollar  bill,  2  5-dollar  bills,  3  silver  dollars,  3 
quarters,  and  2  dimes? 

c.  3  20-dollar  bills,  6  5~-dollar  bills,  2  1-dollar  bills,  2 
half  dollar  bills,  5  dimes,  and  6  nickels? 

d.  5  10-dollar  bills,  10  2-dollar  bills,  1  5-dollar  gold 
piece,  6  half  dollars,  8  dimes,  and  5  cents? 

How  many  half  dollars  are  therein  $2?  $5?  $10?   $12? 
How  many  quarters  are  there  in  $2?     $3?     $5?     $10? 
How  many  dimes  are  there  in  $2?     $3?     $5?     $15? 
How  many  quarters  are  there  in  2  half  dollars?     5  half 
dollars?     12  half  dollars? 


ORAL    EXERCISES. 


177 


How  many  dimes  are  there  in  2  quarters  ?  2  half  dollars  ? 
6  quarters?  3  half  dollars? 

How  many  dimes  are  therein  30*?  80*?  120*?  250*? 
10  nickels? 

How  many  dollars  are  there  in  20  dimes?  50  dimes? 
60  dimes?  75  dimes?  40  nickels?  600  cents? 


257.    Copy  and  complete: 

i    of  $1  =  50* 
i    of  $1 = 
I    of  $1 = 
£    of  $1  = 

•A-  ^  $1  = 


25*  = 


of  $1 
of  $1 
of  $1 
of  $1 
of  $1 


258.    Two  dollars  and  <a  half  means  $2.50;  a  dollar  and 
a  quarter  means  $1.25. 


Complete  and  read: 

$1  +  4  of  $1  = 

$2  +  i  of  $1  = 
$5  +  i  of  $1  - 
$3  +  t  of  $1  = 


$4  +  £    of  $1  = 
$7  +  TV  of  $1  = 

$9  +  -A-  of  $1  = 


259.    Find  the  amount  of  this  bill: 


6  Ib.  steak  at       ....     $  .15 
5  yd.  silk  at  1.35 

4  gal.  milk  at      30 
9  doz.  eggs  at     ....          .14 

178  SCHOOL    ARITHMETIC. 

260.  A  lady  bought  3  Ib.  of  sugar  for  18  cents,  and 
gave  the  grocer  a  half  dollar.  He  made  the  "  change  " 
as  follows: 

Saying  18,  he  handed  her  2#,  and  said  20;  gave  her  a 
nickel,  and  said  25;  then  gave  her  a  quarter,  and  said  50. 
Did  she  get  the  correct  change? 

Change  is  usually  made  by  counting  up  from  the 
amount  of  the  purchase  to  the  amount  given  in  pay- 
ment. 

Find  the  change  by  counting  up: 

Bought  candy  for  3^;  gave  a  dime  in  payment. 
Bought  sugar  for  83^;  gave  $1  in  payment. 
Bought  shoes  for  $3.25;  gave  $5  in  payment. 
Bought  books  for  $8.12;  gave  $10  in  payment. 


NUMBERS    TO    MILLIONS.  179 


NUMBERS  TO  MILLIONS. 

261.  Measure    with    the    quart    measure  the  water  in 
this  pail.     How  many  quarts    are    there?     One    quart  is 
called  the  unit  of  measure. 

Measure  with  a  ruler  the  length  of  your  book.  How 
many  inches  long  is  it?  What  unit  of  measure  did  you 
use? 

When  we  say  w©  have  ten  apples,  the  unit  used  in  count- 
ing them  is  one  apple. 

One  of  any  kind  (or  any  group  regarded  as  one)  by  com- 
parison with  which  we  count  or  measure  is  called  a  unit. 

262.  You  have  already  learned  that  when  three  figures 
are  written  side  by  side,  the  one  at  the  right  represents 
ones,  the  second  figure  represents  tens,  and  the  one  at  the 
left  represents  hundreds. 

Can  you  write  10  hundred  with  three  figures? 
The  number  10  hundred  is  called  a  thousand. 
A  thousand  is  written  —  1,000.    Then  how  many  figures 
are  required  to  write  thousands? 

263.  One  thousand  one  hundred  is  written  — 1,100. 
Twenty-five  thousand  is  written  —  25,000. 

Ten  thousand  five  hundred  is  written  — 10,500. 

One  hundred  twenty  thousand  three  hundred  is  writ- 
ten—  120,300. 

How  many  thousands  and  how  many  hundreds  in 
1,500?  2,600?  8,200?  3,800?  9,300?  18/TOO?  115,400? 


180  SCHOOL    ARITHMETIC. 

264.  One  thousand  one  hundred  ten  is  written — 1,110. 
One  thousand  one  hundred  eleven  is  written  — 1,111. 
One  thousand  twenty-five  is  written  — 1,025. 

One  thousand  four  is  written  —  1,004. 

How  many  thousands  and  tens  in  1,130?  1,480? 
2,140?  3,250?  4,890?  7,620?  6,970?  5,710? 

How  many  thousands,  hundreds,  tens,  and  ones  in  1,235? 
1,346?  1,472?  2,125?  3,521?  6,275?  2,017?  12,534? 

Write  in  figures  and  read  all  the  numbers  from  1,002 
to  1,020;  from  10,995  to  11,001;  from  125,090  to  125,160. 

265.  Complete: 

2?743  =  2000  +  700  +  40  +  3  =  2th  +  7h  +  ±i  +  3o 
5,271  = 
1,075  r= 
12,004  = 

25,378  = 

3000  +  500  +  60  +  2  =  Mh  +  6h  +  6t  +  2o  =  3,562. 
6000  +  200  +  70  +  5  = 
5000  +  800  +  20  +  0  = 
4000  +  000  +  50  +  4  = 
8000  +  300  +  00  +  7  = 

266.  Compare  1,  10,  100,  1000. 

How  many  ones  make  1  ten? 

How  many  tens  make  1  hundred? 

How  many  hundreds  make  1  thousand? 

When  1  stands  alone  how  many  ones  does  it  express? 
When  it  stands  at  the  left  of  a  cipher?  At  the  left  of  two 
ciphers  ? 


NUMBERS    TO    MILLIONS.  181 

In  the  number  11  which  1  expresses  the  greater  value? 
How  many  times  as  great?  In  the  number  111? 

REMEMBER :  Any  figure  represents  ten  times  the 
value  it  would  represent  in  the  next  place  to  the  right. 

267.  In  counting  by  ones  the  unit  is  one. 

In  counting  the  tens  of  a  number,  we  may  regard  one 
ten  as  the  unit  for  the  tens. 

May  one  hundred  be  regarded  as  the  unit  for  the 
hundreds  of  a  number? 

The  ones  of  a  number  are  called  units  of  the  first  order, 
or  simply  units;  the  tens  are  called  units  of  the  second 
order;  the  hundreds  are  called  units  of  the  third  order, 
and  so  on. 

268.  One  more  than  999,999  is  1000  thousands,  which 
is  called  a  million,  and  is  written  thus  —  1,000,000. 

When  we  wrote  thousands,  what  did  we  put  after  the 
last  figure  of  the  thousands? 

Do  we  place  a  second  comma  after  the  figure  for 
millions  ? 

Into  groups  of  how  many  figures  each  do  the  commas 
divide  the  figures? 

For  convenience  in  reading  numbers  the  figures  are 
divided  into  groups  of  three  figures  each,  beginning  at  the 
right.  Each  group  is  called  a  period.  The  right-hand 
group  is  called  the  period  of  units,  the  second  group,  the 
period  of  thousands,  the  third  group,  the  period  of 
millions. 


182 


SCHOOL    ARITHMETIC. 


269.    "What  we  have  learned    about    the    manner   of 
writing  numbers  is  shown  in  the  following 


CO 

_- 

1  1 

a 

.2 

•  g     £     o 
W    H    H 

in 

rH   .  IT?     W 

3 

840 

532 

3d 

Y 

2nd 

1st 

Period. 

Period. 

Period. 

Millions 

Thousands 

Units 

The  number  in  the  table  is  read  three  million7   eight 
hundred  forty  thousand,  five  hundred  thirty-two. 

Examine  the  table  and  tell: 

How  many  figures  are  required  to  write  ten-thou- 
sands \  Hundred -thousands  \ 

How  many  figures  are  required  to  write  millions? 
Are  the  tens  and  ones  of  each  group  read  together? 
How  many  figures  has  the  left-hand  group? 
How  many  figures  must  the  other  groups  contain? 

Each  period  has  three  places — ones,  tens,  and  hun- 
dreds. The  first  period  has  ones,  tens,  and  hun- 
dreds of  ones;  the  second  has  ones,  tens,  and 
hundreds  of  thousands;  and  so  on. 


NUMBERS  TO  MILLIONS.  183 

270.  Eead  the  following:  , 

507  101  340  300      999 

2,100  1,310  2,136  3,204     5,060 

6,400  3,240  1,275  6,308  '    8,401 

12,800  15,890  12,581  16,035    14,008 

234,600  616,720  321,476  695,182   999,999 

3,005,008  2,452,320  1,982,200  2,879,079  1,121,001 

Write  in  figures: 

Two  thousand  five  hundred.  Five  thousand  eight  hun- 
dred. Four  thousand  two  hundred  ten.  Six  thousand  one 
hundred  ninety.  Three  thousand  four  hundred  forty-six. 
Eight  thousand  seven  hundred  thirty-five.  Four  thousand 
three  hundred  eight.  Nine  thousand  twenty-four.  Two 
thousand  ten.  Six  thousand  twenty.  Seven  thousand  five. 
Ten  thousand  fifty-eight.  Eight  thousand  two  hundred 
six.  One  million. 

271.  I         V         X         L         C         D         M 

1  5          10         50       100       500       1000 

You  have  already  learned  how  numbers  are  written  in 
the  Roman  notation  up  to  12. 

Now  state  what  the  new  letters  L,  C,  D,  and  M  each 
stand  for. 

I  represents  1;  II  represents  2;  X  stands  for  10;  XX 
stands  for  20.  Then  what  is  the  effect  of  repeating  a  letter? 

Y  stands  for  5;  IY  stands  for  4;  X  stands  for  10;  IX 
stands  for  9.  "What  then  is  the  effect  of  writing  a  letter  of 
less  value  before  a  greater? 


184:  SCHOOL   ARITHMETIC. 

What  does  XL  stand  for?    XC? 

YI  stands  for  6;  XI  stands  for  11.     What  is  the  effect 
of  writing  a  letter  of  less  value  after  a  greater? 
What  does  LX  stand  for?     CX? 

Complete : 


1=  I 

11  —  XI 

21  =  XXI 

35  =  XXXV 

2  = 

12  = 

22  = 

45  = 

3  = 

13  = 

23  = 

75  = 

4  = 

14  = 

24  = 

95  = 

5  = 

15  — 

25  = 

34  = 

6  = 

16  = 

26  = 

46  = 

7  = 

17  = 

27  = 

77  = 

8  = 

18  = 

28  = 

88  = 

9  = 

19  = 

29  = 

99  = 

20=  30=  101  = 

Addition  and  Subtraction. 


272.   Add 


1 

2 

3 

4 

5 

3,725 

7,618 

5,392 

6,728 

8,796 

5,287 

4,376 

2,763 

8,276 

6,978 

7,392 

2,914 

4,827 

4,937 

3,547 

6 

7 

8 

9 

10 

$7,246 

$2769 

$3486 

$16.38 

$70.35 

3,983 

8478 

7615 

29.15 

25.97 

2,762 

9192 

5307 

85.72 

64.78 

6,219 

7581 

8590 

72.40 

59.24 

8,768 

4803 

6925 

69.17 

91.39 

ADDITION    AND    SUBTRACTION. 


185 


11 

12 

13 

14 

15 

87535 

29413 

44777 

67890 

36925 

62914 

72694 

32416 

12345 

81470 

4728 

547 

87324 

34251 

14703 

872 

84062 

4715 

26076 

69258 

53389 

7618 

982 

8907 

58147 

7604 

385 

5639 

73529 

3692 

5881 

92764 

76248 

982 

81470 

3627 

8270 

39571 

8076 

369 

98376 

64936 

50867 

93745 

70487 

273.    Find  the.  sum  of: 

16.  72384  +  2984  +  37038  +  920  +  8006. 

17.  60572  +  3751  +  807  +  73092  +  46075. 

18.  19283  +  47650  +  2006  +  8372  +  50098. 

19.  53761  +  6807  +  924  +  7354  +  89763. 

20.  40516  +  27385  +  6607  +  4481  +  90876. 

21.  Four  thousand  six,  twenty  thousand  seven  hundred 
fourteen,   eighty-nine,   five  hundred  ninety-four,   eighty- 
four  thousand  nineteen. 


274.  Subtract: 

1 

2 

3 

4 

5 

7,236 
4,753 

5,176 
2,849 

8,352 
5,178 

6015 
2376 

9200 
2914 

6 

7 

8 

9 

10 

$3520 
1750 

$7245 
2754 

$6321 
4576 

$4000 
2545 

$8007 
7129 

11 

12 

13 

14 

15 

8003 
2347 

6004 
5706 

7005 
5717 

3004 
1068 

45216 

27089 

186 


SCHOOL    ARITHMETIC. 


16 

17 

18      19 

20 

37002 

56214 

73014    18001 

20450 

19008 

42657 

34025     7608 

16784 

21 

22 

23 

24 

870623 

601540 

803002 

500000 

581539 

403862 

80305 

423167 

275.  The  Minuend  is  the  number  from  which  another 
number  is  subtracted;  the  Subtrahend  is  the  number  that 
is  subtracted.     What  is  ihej'emainder  f 

1.  The  minuend  is  825,  the  subtrahend  is  368.     Find 
the  remainder. 

2.  The  minuend  is  7215,  the  remainder  2345.   What  is 
the  subtrahend? 

3.  The  subtrahend  is  4527,  the    remainder    is    1328. 
What  is  the  minuend? 

4.  To  what  number  must  572  be  added  to  make  the 
sum  1420? 

5.  If    365    be    subtracted  from  -     — ,  the  remainder 
will  be  1824. 

276.  1.      There  are  365  days  in  a  common  year.     In 
10  common  years  there  are  -     -  days. 

2.  In  1860  there  were  177,840  people  living  in  Boston; 
in  1890,  there  were  448,477.     What  was  the  increase  in 
30  years? 

3.  From  1860  to  1890  the  population  of  Baltimore 
grew  from  212,418  to  434,439.     Find  the  gain. 

4.  In  1890  how  much  larger  was  the  population  of 
Boston  than  that  of  Baltimore? 


ILLUSTRATION.  $5  -f  $5  -f  $5  -f-  $5  =  $20.  This  is  addition. 
4  X  $5  ==  $20.  This  is  multiplication.  $5  is  the  multiplicand.  It  is 
taken  4  times,  hence  4  is  the  multiplier.  Which  is  the  product? 

The  multiplicand  and  the  multiplier  are  called  factors 
of  the  product.  Thus,  in  2  X  5  =  10,  2  and  5  are  factors 
of  10. 

Of  what  number  are  8  and  11  the  factors?     5  and  7? 

One  factor  of  21  is  3.     What  is  the  other  factor? 

What  is  the  product  of  the  factors  7  and  9?    10  and  12? 

The  product  is  48,  and  one  factor  is  4.  What  is  the 
other  factor? 


279. 

1 

Find  the  products: 

20 
9 

4 

5 

$1250 
5 

$2348           $3176 
3                    4 

$5267 
6 

$24,639 
5 

6 

7                   8 

9 

10 

6314 

7 

11 

8273 
9 

5283              7489 
6                  7 

36,458 
•      6 

57,926 
8 

12                 13 

6742             9275 

8                   8 

14 
7364 
9 

15 

69,078 
9 

MULTIPLICATION.  189 


16                 17 

18                    19 

20 

3906             4075 

8                 '    9 

7766              8594 

7                   8 

99,888 
9 

21                  22 

23                    24 

25 

5604             3817 
6                    8 

6670              4096 

9                    7 

124,762 
6 

26.     Multiplier  8, 
27.     Multiplicand 

multiplicand  50,725. 
23,450,  multiplier  7. 

28(K     1.     If  a  man  earns  $125  a  month,  how  much 
does  he  earn  in  6  months? 

$125  in  one  month. 

6  In  6  months  he  earns  6  times 

$125,  or  $750. 
$•750  in  six  months. 

2.  A  grocer  bought  8  barrels  of  sugar  each  weighing 
284  Ib.     How  many  pounds  did  he  buy? 

3.  Mr.  Henry  pays  $425  a  year  for  rent.     How  much 
does  he  pay  in  3  years? 

4.  If  a  teacher  is  paid  $270  each  year,  how  much  is 
paid  in  8  years? 

5.  How  many  strokes  does  a  clock  strike  in  12  hours? 
In  24  hours?    In  a  week? 

6.  If  a  train  runs  386  miles  a  day,  how  far  does  it 
run  in  7  days? 

7.  The  distance  from  Pit.tsburg  to  Philadelphia  is  354 
miles.     How  many  miles  does  a  man  travel  who  makes 
2  round  trips  between  the  two  cities? 

8.  A  man  sold  48  bales  of  cotton,  which  was  TV  of  his 
crop.     How  many  bales  had  he  left? 


190  SCHOOL    ARITHMETIC. 

281.     1.     Multiply  $48  by  12. 

$48 
12 

~~QA  -         O   V  Are  2  times  $48  +  10  times 

480  =  10  X 


$576  =  12  X 

2.  Multiply  $32,  $54,  $66,  and  $75  each  by  12. 

3.  Multiply  225  by  15.     By  23. 

225  225 

15  23 


1125=    5X225  675=    3X225 

2250  =  10  X  225  .  4500  =  20  X  225 

3375  =  15  X  225  5175  =  23  X  225 

4.     Multiply  314  by  13.     By  24. 
Find  the  produces: 

5.  36  X  12.  10.  124  X  22.  15.     413  X  18. 

6.  45  X  13.  11.  143  X  25.  16.     625  X  23. 

7.  63  X  15.  12.  216  X  32.  17.     842  X  26. 

8.  72  X  18.  13.  244  X  36.  18.     736  X  33. 

9.  88  X  23.  14.  326  X  43.  19.     534  X  44. 

20.     Multiply  648  by  164. 

648  648 

164  164 


2592=  4X648  2592 
38880=  60  X  648  3888* 
64800  =  100  X  648  648 


106272  =  164  X  648       106272 

*  In  multiplying  by  tens  it  is  not  customary  to  put  the  0  in  ones' 
place.  60  X  648  =  38880  ones,  or  3888  tens. 

In  multiplying  by  hundreds  how  many  ciphers  may  we  omit? 
When  we  multiply  by  tens  and  omit  the  0,  in  what  place  does  the 


MULTIPLICATION.  191 

first  figure  of  the  partial  product  stand  ?    In  what  place  when  we 
multiply  by  hundreds  and  omit  the  two  ciphers? 

Observe  that  the  ones,  tens,  and  hundreds  of  the  multiplicand,  in  order, 
are  multiplied  by  the  ones,  tens,  and  hundreds  of  the  multiplier,  in  order, 
and  that  the  first  figure  of  each  product  is  put  directly  under  the  figure  of 
the  multiplier  used  in  obtaining  it,  and  that  the  products  are  then  added. 


282.  Multiply: 

1 

2 

3      4 

5 

362 

264 

218     264 

317 

24 

26 

32      34 

25 

7 

8 

9      10 

11 

523 

417 

643     527 

486 

44 

35 

38      46 

53 

13 

14 

15 

16 

5247 

6351 

2583 

4286 

54 

68 

65 

73 

18 

19 

20 

21 

6304 

7023 

5230 

4076 

36 

47 

84 

63 

23 

24 

25 

26 

325 

761 

248 

691 

143 

235 

534 

346 

28 

29 

30 

31 

2317 

3465 

4263 

6375 

324 

125 

217 

264 

27 

835 
462 

32 

8729 
536 

33.     Multiply  325  by  103. 
325 

If  either  factor  is  0,  what  is  the  product? 
Multiply    103    by  325   and    compare    the 
products. 


33475 


192 


SCHOOL    ARITHMETIC. 


283.  Find  the 

product  : 

1.  7430  X  53. 

10.  2108  X  93. 

19.  62425  X  55. 

2.  9625  X  49. 

11.  3206  X  57. 

20.  23507  X  68. 

3.  6275  X  56. 

12.  4004  X  68. 

21.  75310  X  39. 

4.  4760  X  72. 

13.  5760  X  74. 

22.  38672  X  74. 

5.  3586  X  63. 

14.  3090  X  85. 

23.  50836  X  83. 

6.  8274  X  76. 

15.  6805  X  39. 

24.  40078  X  95. 

7.  6407  X  81. 

16.  7273  X  47. 

25.  82036  X  78. 

8.  496  X  237. 

17.  638  X  524. 

26.  3726  X  485. 

9.  738  X  346. 

18.  857  X  432. 

27.  4385  X  724. 

284.     1.    Multiply  72  by  30. 

72  72 


30      or 


30 


2160 


2160 


Here  we  multiply  by  3  tens 
and  no  ones. 


Multiply  : 

2.       74  X  20. 
3.       48  X  30. 
4.       65  X  40. 
5.     142  X  30. 

6.       59  X  30. 

7.       38  X  60. 
8.       67  X  50. 
9.     234  X  40. 

10.     75  X    80. 
11.     83  X     70. 
12.     96  X    90. 
13.  456  X  150. 

285.     1.     If    a    man    takes    180    steps  a  minute,  how 
many  steps  will  he  take  in  an  hour? 

2.  If  a  train  runs  35  miles  an  hour,  how  far  will  it 
run  in  20  hours? 

3.  How  much  will  8  months'  wages  amount  to  at  $27 
a  month? 

4.  When  you  know  the  cost  of  one  orange,  how  can 
you  find  the  cost  of  10  oranges? 

5.  A  steamer  sails  275  miles  a  day.    How  far  does  she 
sail  in  9  days? 


MULTIPLICATION.  193 

6.  In  an  orchard  there  are  18  rows  and  12  trees  in  a 
row.    How  many  trees  in  the  orchard? 

7.  My  parlor  is  18  feet  square.     How  many  square 
yards  of  carpet  will  it  require? 

8.  How  many  lines  are  there  on  this  page  of  your 
book?    How  many  on  27  such  pages? 

9.  There  are  144  pens  in  a  box.     How  many  pens  in 
2  dozen  boxes? 

10.  A  lot  is  175  feet  long  and  60  feet  wide.     How 
many  square  feet  does  it  contain? 

11.  There  are  28  regiments  in  an  army.    If  there  are 
875  men  in  each  regiment,  how  many  men  in  the  army? 

12.  If  a  bushel  of  wheat  weighs  60  pounds,  what  will 
150  bushels  weigh? 

13.  An  army  used  48512  pounds  of  meat  each  week. 
How  much  was  used  in  13  weeks? 

Find  the  cost  of: 

14.  245  dozen  fresh  eggs  at  9^  a  dozen. 

15.  384  pounds  of  sugar  at  6^  a  pound. 

16.  18  pianos  at  $275  each. 

17.  75  tons  of  clover  hay  at  $14  a  ton. 

18.  286  bushels  of  wheat  at  70^  a  bushel. 

19.  524  sheep  at  $4  a  head. 

20.  4  barrels  of  molasses,  42  gal.  each,  at  35^  a 
gallon. 

21.  65  barrels  of  apples,  3  bu.  each,  at  45^  a  bushel. 

22.  2  rolls  of  carpet,  59  yd.  each,  at  75^  a  yard. 

23.  8  loads  of  coal,  45  bu.  each,  at  8^  a  bushel. 


194  SCHOOL    ARITHMETIC. 

Division. 

286.  When    we    divide    one    number  by  another,  the 
result  is  called  the  Quotient ;  the  number  divided  is  called 
the  Dividend;  and  the  number  by  which  we  divide  is  called 
the  Divisor. 

In  multiplication  we  have  two  factors  to  find  the  product. 
In  division  we  have  a  product  and  one  factor  to  find  the 
other  factor.  The  dividend  is  the  product,  the  divisor 
one  factor.  What  is  the  other  factor? 

2X$5  =  $10.        $10  -r-2  =  $5.        $10 -^-$5  =  2, 

Point  out  the  factors  in  this  example.  The  product. 
The  dividend.  The  divisors.  The  quotients. 

287.  Division  includes — 

(A).  Finding  one  of  the  equal  parts  of  a  number;  as,  -J 
/of  $10  =  $5.  $10  -f-  2  =  $5. 

(B).  Finding  how  many  times  one  number  contains 
.another;  as,  $20  -r-  $5  =  4.  12  ft.  -4-  3  ft.  ==  4. 

1.  What  is  one  of  the  3  equal  parts  of  $24? 

$24  -r-  3  =  $8. 

2.  How  many  times  is  $3  contained  in  $24? 

$24  -=-$3  =  8. 

In  these  examples  $24  is  the  dividend.  In  the  first  3  is  the  divisor 
and  $8  the  quotient.  In  the  second  $3  is  the  divisor  and  8  the 
quotient. 

3.  When  50  Ib.  is  the  dividend  and  5  the  divisor,  what 
is  the  quotient? 

What  is  required  in  this  example  ?  Do  we  also  find  the  number  of 
pounds  in  each  part?  Is  the  quotient  of  the  same  kind  (pounds)  as 
the  dividend? 


DIVISION. 


195 


4.  When  40^  is  the  dividend  and  5^  the  divisor,  what 
is  the  quotient? 

Are  the  dividend  and  divisor  of  the  same  kind  in  this  example? 
Does  the  quotient  denote  the  number  of  times  the  divisor  must  be 
taken  to  equal  the  dividend? 

5.  Find  by  trial  whether  the  product  of  the  quotient 
and  divisor  is  equal  to  the  dividend. 

6.  When  $36  is  the  dividend  and  $4  the  quotient,  what 
is  the  divisor? 

7.  When  $7  is  the  divisor  and  5  the  quotient,  what  is 
the  dividend? 

8.  If  you  have  a  dozen  eggs  and  wish  to  give  me  J  of 
them,  you  must  give  me  one  of  the  3  equal  parts  of  12 
eggs.    That  is,  you  must  divide  12  eggs  by  3. 

9.  Divide  30  gallons  by  3.     By  5.     By  6.     By  10. 

10.  What  is  4  of  36  feet?    J?  \l     TV? 

288.    Divide: 
12  3  45  6 

3)  369   5)  550   6) 126   5)  205   4) 328    6)  426 


7 
4)368 


8 

5)400 


9 

7)427 


10 

6)  540 


11 

8)720 


12 

8)818 


13  14  15  16 

6)  612        7)  714       5)  300        9)  36 


17  18 

8)  808        9)  918 


19 

4)  8044 


20 

5)  1050 


21 

3) 9126 


22 

6)  1206 


23 

7)14014 


289.    Find  the  quotients: 


1. 

3096- 

-3. 

7. 

18618- 

-6. 

13. 

305100- 

-5. 

2. 

4015- 

-5. 

8. 

20515  - 

-5. 

14. 

180120- 

-3. 

3. 

1421- 

-7. 

9. 

16812- 

-4. 

15. 

363636- 

-6. 

4. 

1224- 

-6. 

10. 

14721  - 

-7. 

16. 

281435  - 

-9. 

5. 

1612- 

-4. 

11. 

24816- 

-8. 

17. 

271836  - 

-9. 

6. 

3240- 

-8. 

12. 

18924- 

-9. 

18. 

321632- 

-8. 

196  SCHOOL    ARITHMETIC. 

19.  What  is  the  difference  between  i  of  824  and  824 
-5-  4? 

20.  Which  would  you  rather  have  —  i  of  $1200  or 
$1200-^-  3? 

290.    Are  5  tens  and  6  ones  equal  to  4  tens  and  16  ones? 
Complete : 

34  =    3  tens  +  4  ones  =  2  tens  + ones. 

78  =    7  tens  +  8  ones  =  6  tens  +  -      -  ones. 

42  =    4  tens  +  2  ones  =  3  tens  + ones. 

87  =    8  tens  +  7  ones  =  6  tens  +  —  -  ones. 

95  =    9  tens  +  5  ones  =  5  tens  + ones. 

126  =  12  tens  +  6  ones  =  7  tens  +  -       -  ones. 

1.     Divide  34  by  2,  or  find  i  of  34. 

2)  34  =  2  tens  +  14  ones.          j  Of  2  tens- 1  ten. 
17  =  1  ten    +    7  ones.          i  of  14  ones  -  7  ones. 


Complete: 

2.     4  of  78  = 

6. 

|  of  126  = 

10.     76-^-2 

3.     J  of  42  = 

7. 

i  of     52  = 

11.     51  -f-  3 

4.     ^  of  87  = 

8. 

i  of     65  = 

12.     80  -H  5 

5.     4  of  95  = 

9. 

i  of     64  = 

13.     78  -T-  6 

291.     1.     Divide  968  by  8. 

8)968  =  Sh  +  16*  +  So 
121  =  1ft  +    2*  +  lo 


Divide  : 

2. 

568 

by 

4. 

6. 

655 

by 

5. 

10. 

516 

by 

3. 

3. 

605 

by 

5. 

7. 

968 

by 

8. 

11. 

750 

by 

5. 

4. 

847 

by 

7. 

8. 

780 

by 

6. 

12. 

684 

by 

4. 

5. 

726 

by 

6. 

9. 

648 

by 

4. 

13. 

846 

by 

6. 

DIVISION.  19T 

292.     1.     Divide  945  by  7. 

7)945  =  =  7/i  +  2±t  +  5o=  7fe  +  21*  +  35o 
135  =  Ife  +    3*  +    5o 

9/1  -r-  7  =  Ih,  and  2ft  or  20*  remaining;  24*  --5-  7  =  3«,  and  3?  or 
30  o  remaining  ;  35  o  -f-  7  =  5  o. 


'Divide  : 

2                3 

456 

7 

5)  625        4)  548 

3)  525        6)  756        5)  725 

4)632 

8                9 

10              11               12 

13 

6)  852        3)  534 

8)  984       7)  952        8)  992 

6)948 

14                 15 

16                   17 

18 

4)  8524         3)  6471 

2)  2756         5)  5620 

6)  6804 

19                 20 

21                   22 

23 

4)  9256         3)  7260 

2)  3674         5)  6705 

6)  7344 

293.    1.     Divide 

7356  by  12. 

(a) 
12)  7356 

613 

w 

12)  7356  (  613 
72 

quotient. 

73  hundreds  +-  12  =  6  hundreds, 

and  1  hundred  remaining. 
15  tens  -5-  12  =  1  ten,  and  3  tens  35 

remaining.  og 

36  ones  -r-  12  =  3  ones. 

A  common  way  of  proceeding  is  something  like  the  following : 
12  in  73  6  times  and  1  over ;  12  in  15  once  and  3  over ;  12  in  36  3 
times. 

The  process  as  shown  in  (a)  is  called  short  division;  as  shown  in 
(b)  is  long  division.  Wherein  do  they  differ?  In  what  ways  are 
they  alike? 


198  SCHOOL    AEITHMETIC. 

2.  Divide  864  by  24. 


24)  864  (36 

72 

144 
144 


86  tens  ^-  24  =  3  tens  and  a  remainder.  24  X  3 
tens  =  72  tens.  14  tens  and  4  ones  are  144  ones. 
144  ones  -f-  24  —  6  ones.  24  X  6  ones  =  144  ones. 


Find  the  quotients: 

3.  5670—    6. 

4.  7212—    6. 

5.  6315—    5. 

6.  3507—    7. 

7.  2536—    8. 

8.  9208—    8. 

9.  7452  —  12. 

10.  3744  —  12'. 

11.  4956  —  12. 

12.  6276  —  12. 


13. 

3454- 

-11. 

23. 

7072- 

-52. 

14. 

4565- 

-11. 

24. 

3536- 

-26. 

15. 

4851- 

-21. 

25. 

5346- 

-22. 

16. 

9702- 

-21. 

26. 

14624- 

-32. 

17. 

3844- 

-31. 

27. 

14616- 

-42. 

18. 

7688- 

-31. 

28. 

25599- 

-53. 

19. 

9963- 

-41. 

29. 

62350- 

-25. 

20. 

7488- 

-24. 

30. 

20020  - 

-35. 

21. 

6908- 

-22. 

31. 

10368- 

-36. 

22. 

9050- 

-25. 

32. 

30576- 

-48. 

294.     1. 

2)  $49 


Find  one  half  of 

=  $40  +  $9 


^  of  4  tens,  or  $40,  =  $20. 
$  of  9  ones,  or  $9,  =  $4£,  or 

$4.50. 

When  there  is  a  remainder  we  may  write  the  quotient  and  re- 
mainder as  a  complete  quotient,  as  $24£  above. 


Find: 


2.  i 

3.  J  of  10  yd. 

4.  ^  of  45  qt. 

5.  J  of  75  bu. 
6. 


7.  iof  45  gal. 

8.  Jofl5pk. 

9.  iof  69  bu. 

10.  -^  of  $21. 

11.  iof  145  Ib. 


12.  Jof  127. 

13.  J  of  214. 

14.  iof  366. 

15.  |  of  329. 

16.  TVof  501. 


DIVISION.  199 

295.     1.     At  60^  a  gallon,  what  is  the  value  of  a  quart 
of  molasses? 

2.  How  many  times  can  you  fill  an  8-gallon  jug  from  a 
barrel  that  holds  48  gallons? 

3.  A  crate  holds  1728  eggs.     How  many  dozen  eggs 
are  there  in  the  crate? 

4.  When  you  know  the  cost  of  10  apples,  how  can  you 
find  the  cost  of  one  apple? 

5.  A  cattle  dealer  paid  $682  for  22  head  of  cattle. 
What  was  the  average  price? 

6.  How  many  years  old  is  a  man  who  has  lived  900 
months  ? 

7.  Tommy  Jones  weighs  100  Ib.    A  ton  of  hay  weighs 
as  much  as  20  such  boys.     How  many  pounds  in  a  ton? 

8.  If  .there  are  60,000  Ib.  of  coal  in  a  car,  how  many 
tons  are  in  it? 

9.  A  nine-acre    field    produced    375    bushels  of  oats. 
How  many  bushels  to  the  acre  did  it  yield? 

10.  In  4  years  the  President  receives  salary  to  the 
amount  of  $200,000.     What  is  his  yearly  salary? 

11.  There  are  5280  ft.  in  a  mile.     How  many  yards 
in  a  mile? 

12.  If  a  man  saves  $12  a  month,  in  how  many  months 
will  he  save  $1440?     In  how  many  years? 

13.  One  day  the  fares  on  a  certain  street  car  amounted 
to  2450  cents.     Each  passenger  paid  5  cents.     How  many 
persons  rode  on  the  car  that  day? 

14.  If  a  man  on  a  bicycle  rides  48  miles  each  day  in 
June,  how  much  farther  will  he  have  to  travel  to  make 
1500  miles? 

15.  Mr.  Butler  divided  $19500  equally  among  his  3 
children.     The  daughter  divided  her  share  equally  among 
her  5  children.     How  much  did  each  grandchild  get? 


200  SCHOOL    ARITHMETIC. 

REVIEW    WORK. 
Oral  Exercises. 

296.    1.     If  6  oranges    cost    30    cents,    what    will  3 
oranges  cost? 

If  6  oranges  cost  30  ct.,  1  orange  will  cost  £  of  30  ct.,  or  5  ct.;  and 
3  oranges  will  cost  3  X  5  ct.,  or  15  ct. 

2.  If  9  cords  of  wood  cost  $36,  what  will  1  cord  cost? 
What  will  12  cords  cost? 

3.  If  4  knives  cost  96  cents,  what  will  9  knives  cost? 

4.  If  -i  of  a  pound  of  candy  costs  10  cents,  how  much 
must  I  pay  for  2  pounds? 

5.  If  -J  of  a  pound  of  cheese  costs  5  cents,  how  much 
will  2  pounds  cost? 

6.  If  4  men  can  do  a  piece  of  work  in  6  days,  how  many 
days  will  it  take  3  men  to  do  it? 

If  it  takes  4  men  6  days  to  do  the  work,  it  will  take  1  man  4X6 
days,  or  24  days  ;  if  it  takes  1  man  24  days,  it  will  take  3  men  £  of 
24  days,  or  8  days. 

7.  If  8  men  can  mow  a  field  in  9  days,  how  many  days 
will  it  take  6  men  to  mow  the  field? 

8.  If  4  men  can  dig  a  ditch  in  5  days,  how  many  men 
will  be  required  to  dig  it  in  4  days? 

9.  T  is  1  of  what  number? 

10.  At  10  cents  a  dozen,  what  will  60  apples  cost? 

11.  How  many  oranges  at  the  rate  of  2  for  5  cents 
can  I  buy  for  20  cents? 

12.  How  many  coats  can.be  cut  from  21  yards  of  cloth, 
if  3  coats  can  be  cut  from  9  yards? 

13.  How  many  pounds  of  sugar  at  6  cents  a  pound 
must  be  given  for  2  pounds  of  coffee  at  15  cents  a  pound? 

14.  If  you  divide  36  marbles  among  6  boys,  how  many 
marbles  will  2  boys  have? 


WRITTEN    EXERCISES.  201 

15.  If  a  railroad  car  has  8  wheels,  how  many  cars  will 
40  wheels  supply? 

16.  A  boy  bought  6  lead  pencils  at  4^  each  and  ex- 
changed them  for  erasers  at  3^  each.     How  many  erasers 
did  he  get? 

17.  If  7  men  can  do  a  piece  of  work  in  9  days,  how 
many  men  will  it  take  to  do  the  same  work  in  1  day? 

18.  If  you  buy  3  dozen  pencils  at  20^  a  dozen,  and  sell 
them  at  3^  each,  how  much  do  you  gain? 

19.  John  is  9  years  old,  and  his  father  is  3  times  as  old 
and  9  years  more.     How  old  is  his  father? 

20.  If  a  man  pays  $30  for  6  sheep,  how  much  at  the 
same  rate  does  he  pay  for  5  sheep? 

21.  How  many  square  yards  in  the  floor  of  a  room  15 
yards  long  and  9  yards  wide? 

22.  Alice's  father  gave  her  $2  every  2  months.     How 
many  dollars  did  he  give  her  in  a  year? 

23.  If  a  cow  gives  6  qt.  of  milk  a  day,  how  many 
gallons  does  she  give  in  six  days? 

24.  $28  is  $7  more  than  the  cost  of  3  tons  of  coal. 
What  does  1  ton  cost? 

25.  A  man  pays  $3  a  month  for  his  room  rent  and  $9 
a  month  for  his  office  rent.     How  much  rent  does  he  pay 
a  year? 

26.  If  2  oranges  are  worth  4  apples,  how  many  oranges 
are  worth  12  apples? 

Written  Exercises. 

297.  .  1.  A  man  gave  $35  for  a  wagon,  and  paid  $4 
for  repairing  it.  For  how  much  must  he  sell  it  to  gain 
$11? 

2.  There  are  CL  Psalms.     When  you  have  read  XC, 
how  many  more  have  you  to  read? 

3.  The  earth  moves  in  its  orbit  19  miles  a  second.  How 
manv  miles  does  it  move  a  minute? 


202       .  SCHOOL    ARITHMETIC. 

4.  B  and  C  start  from  the  same  place  and  travel  in 
opposite  directions.     B  travels  5  miles  an  hour,  and  C  4 
miles  an  hour.     How  far  apart  are  they  in  15  hours? 

5.  A  clock  strikes  156  times  a  day.    How  often  will  it 
strike  in  a  year  of  365  days? 

6.  A  barrel  of  flour  weighs  196  pounds.     What  is  the 
weight  of  J  a  barrel? 

7.  Sound  travels  1120  feet  a  second.    How  far  off  is  a 
cannon,  the  report  of  which  is  heard  in  13  seconds? 

8.  How  many  times  will  500  oranges  fill  a  fruit  dish 
that  holds  1  dozen  oranges,  and  how  many  will  be  left 
over? 

9.  If  you  purchase  a  horse  for  $100,  and  pay  $40  in 
cash,  how  long  must  you  work  at  the  rate  of  $12  a  week 
to  pay  the  balance? 

10.  If  your  pulse  beats  4320  times  in  an  hour,  how 
many  times  will  it  beat  in  a  day? 

11.  In  what  number  is  225  contained  25  times? 

12.  Gold  was  discovered  in  California  in  1848.     How 
many  years  ago  was  that? 

13.  A  farmer  sold  60  bushels  of  apples  at  $2  a  bushel. 
How  many  pigs  can  he  buy  at  $4  each  with  the  money? 

14.  One  farmer  gets  $200  for  his  wood,  and  his  neigh- 
bor gets  $248.     The  price  is  $8  a  cord.     How  many  cords 
do  they  both  sell  ? 

15.  A  boy  takes  9  subscriptions  to  the  "  Youth's  Com- 
panion "  at  $1.75  each.    How  much  money  does  he  receive 
for  them  all? 

16.  A  building  is  240  feet  long  and  200  feet  wide. 
How  many  yards  is  it  around  the  building? 

17.  A  man  owed  $5000.     He  made  three  payments, 
one  of  $1375,  another  of  $964,  and  another  of  $2484. 
How  much  did  he  still  owe? 


WRITTEN    EXERCISES.  203 

18.  A  car  line  is  12  miles  long.     If  a  car  makes  6 
round  trips  daily,  how  many  miles  will  it  run  during  the 
month  of  July? 

19.  If  8  cords  of  wood  are  worth  $32,  what  are  19 
cords  worth? 

20.  America  was  discovered  in  1492;    the    Pilgrims 
landed  at  Plymouth  in  1620.     How  many  years  from  the 
discovery  of  America  to  the  landing  of  the  Pilgrims? 

21.  A  man  paid  $175  for  a  horse,  which  was  5  tinies 
as  much  as  he  paid  for  a  cow.     How  much  did  he  pay 
for  both?  • 

22.  The  multiplicand  was  3962;    the    multiplier  was 
186.     What  was  the  product? 

23.  If  the  divisor  is  55,  and  the  dividend  is  9625,  what 
is  the  quotient? 

24.  The  floor  of  a  room  16  ft.  long  contains  192  square 
feet.     What  is  the  width? 

25.  How  many  marble  slabs  each  10  in.  by  2  ft.  will 
cover  a  floor  10  ft.  square? 

26.  A  baker  has  200  loaves  of  bread.     He  sells  f  of 
them  at  6^  each,  and  the  remainder    at    5^    each.     How 
much  does  he  get  for  his  bread? 

27.  If  3  oranges  cost  10^',  how  many  times  10^  must 
be  paid  for  a  dozen  oranges? 

28.  A  farmer  clipped  1000  Ib.  of  wool  from  his  sheep. 
If  each  fleece  weighed  5  Ib.,  how  many  sheep  had  he? 

29.  A  sugar  plantation  produces  2000  barrels  of  sugar, 
averaging  250  Ib.  in  weight.     At  2^  a  pound,  what  is  the 
value  of  the  sugar? 

30.  A  man  earns  $2.50  a  day  and  pays  50^  a  day  for 
board.     If  he  does  not  work  on  Sundays,  how  much  will 
he  have  left  this  month  after  paying  his  board? 


204  SCHOOL    ARITHMETIC. 

U.  S.  Money  and  Decimals. 
Ten  dimes  make  a  dollar. 

298.  What  part  of  a  dollar  is  1  dime?  2  dimes?  3 
dimes?  5  dimes?  10  dimes? 

How  many  tenths  of  a  dollar  make  a  dollar? 

How  many  tenths  make  1  one? 

A  dime  is  1  tenth  of  a  dollar.  We  write  dimes  (tenths 
of  dollars)  in  the  first  place  to  the  right  of  dollars. 

Where  with  reference  to  ones'  place  should  we  write 
tenths  of  ones? 

What  do  we  place  between  the  figures  for  dollars  and 
the  figures  for  dimes? 

Should  we  place  the  decimal  point  after  ones  and  before 
tenths  ? 

Tenths  occupy  the  first  place  to  the  right  of  the  decimal 
point. 

The  number  five  and  three-tenths  is  written  5.3. 

The  number  .3,  or  0.3,  is  read  three  tenths. 


299.    What  part  of  a  dollar  is  1  cent? 

How  many  hundredths  of  a  dollar  are  3^?     5^?     10#? 


of  a  dollar=.01  of  a  dollar. 
2^=1.02=^  of  a  dollar  =  .02  of  a  dollar. 

of  a  dollar  =  .05  of  a  dollar. 

of  a  dollar  =  .10  (or  .1)  of  a  dollar. 
20^=1.20  =  ^  of  a  dollar  =  .20  (or  .2)  of  a  dollar. 
25^=1.25  =  of  a  dollar  =  .25  of  a  dollar. 


Which  is  easier  to  wrie,   y-J-g-  of  a  dollar  or  .01  of  a 
dollar? 


U.     S.     MONEY    AND    DECIMALS.  205 

There  are  two  ways  of  writing  hundredths  and  tenths. 

and  .01  are  both  read  one-hundredth. 

and  -05  are  both  read  five-hundredths. 
-fa  and  .1  are  both  read  one-tenth. 
fa  and  .5  are  both  read  five-tenths. 
-fa  and  .2  are  both  r^ad  two-tenths. 

and  .25  -are  both  read  twenty-  five-hundredths. 


300.    How  many  tenths  of  a  dollar    are    10    cents  (1 
dime)? 

How  many  hundredths  of  a  dollar  are  10  cents? 
Then  how  many  hundredths  make  1  tenth? 

10  hundredths  make  1  tenth. 
10  tenths  make  1  one. 

What  is  written  between  tens  and 
tenths  f 

The  places  to  the  right  of  ones  are 
called    decimal    places.     Compare  the 
names    of    the    decimal    places    with 
those  of  the  corresponding  places  on 
the  left  of  the  decimal  point. 
How  many  of  each  place  make  1  of  the  next  place  to 
the  left? 

Does  the  figure  next  to  the  decimal  point  express  tenths 
or  hundredths?    Which  figure  expresses  hundredths? 

When  there  are  five  hundredths  and  no  tenths,  what  is 
written  in  tenths7  place? 

When  there  are  tenths  and  no  hundredths,  is  it  neces- 
sary to  put  a  zero  in  hundredths'  place?    Why  not? 

Is  1  tenth  (.1)  of  a  dollar  equal  to  10  hundredths  of  a 
dollar?    Is  1  dime  equal  to  10  cents? 


206  SCHOOL    ARITHMETIC. 

301.  How  many  dimes  and  cents  in: 

$.05  $.04  $.50  $.25  $.05 

$.20  $.30  $.08  $.05  $.75 

$.25  $.34  $.58  $.30  $.80. 

How  many  tenths  and  hundredths  in: 

.04  .4  .05         *.7  .1  A5 

.2  .03  .6  .05  .35  .12 

.24  .43  .65  .75  .45  .57 

302.  Copy  and  complete: 

4  hundredths  of  a  dollar  ==  4^  =  $.04. 

6  hundredths  of  a  dollar  = 
9  hundredths  of  a  dollar  = 

3  tenths   of  a   dollar  = 

7  tenths   of  a  dollar  = 

2  tenths  and  5  hundredths  of  a  dollar  = 
25  hundredths  of  a  dollar  = 

5  tenths  and  8  hundredths  of  a  dollar  = 

303.  Write  with  the  decimal  point: 

4  hundredths  4  tenths  and  2  hundredths 

7  hundredths  3  tenths  and  6  hundredths 

5  tenths  7  tenths  and  5  hundredths 

8  tenths  1  tenth    and  0  hundredths 
36  hundredths               10  hundredths 

65  hundredths  50  hundredths 

304.  Two  dimes  and  5   cents   are  how  many  cents? 
Two  tenths  and  5  hundredths  are  how  many  hundredths? 

Two  dimes  are  how  many  cents?     Two  tenths  are  how 
many  hundredths? 

How  many  hundredths  of  a  dollar  make  a  dime?  .10=.!. 


U.     S.     MONEY    AND    DECIMALS.  207 

A  quarter  is  equal  to  how  many  hundredths  of  a  dollar? 

A  silver  dollar  is  worth  how  many  hundredths  of  a 

dollar?  How  many  tenths  of  a  dollar?  10  tenths  = 

hundredths. 

How  many  tenths  of  a  dollar  make  a  half  dollar?  How 
many  hundredths?  .5  =  .50. 

75  cents      *       =  7  dimes  and  -     -  cents. 

75  hundredths  —  7  tenths  and hundredths. 


Write  with  the  decimal  point: 


4 


TOT  TOT  100  i  o  TOT 

TOT  TOT  TOT  TO  TOT 

TOT  TOT  ITT  TO"  TOT 

305.    What  part  of  a  dime  is  a  cent? 

One-tenth  of  a  dime  is  what  part  of  a  dollar? 

One-tenth  of  .1  of  $1  is  one  -      -  of  a  dollar. 

Compare  $10  and  $1.     10  ft.  and  1  ft. 

Six  minutes  is  what  part  of  an  hour?     12  minutes? 

How  many  tenths  of  an  hour  are  thirty  minutes? 

What  part  of  $500  is  $50?     $5? 

What  is  .01  of  $100?     Of  $200?     Of  $500? 

One  foot  is  what  part  of  100  feet?    10  feet? 

A  dollar,  3  dimes,  and  2  nickels  are  how  many  tenths 
of  a  dollar? 

Two  dimes,  a  nickel,  and  3  pennies  are  how  many  hun- 
dredths of  a  dollar? 

How  many  ones  in  30  tens?    In  30  tenths? 

How  many  ones  and  tenths  are  there  in  25  tenths? 
Write  it  decimally. 

How  many  ones,  tenths,  and  hundredths  in  each  of 
these:  1.11,  1.05,  .05,  .44,  55.55? 


208  SCHOOL    ARITHMETIC. 

Draw  a  square  and  divide  it  into  10  equal  parts.    Point 
out  .2  of  the  square.     .5  of  it.     .7  of  it. 

Add: 


(a) 
37.5 

w 

26.8 

62.4 

(*) 

81.92 

25.65 

25.6 

34.2 

13.7 

34.34 

43.37 

47.5 

51.3 

45.6 

56.87 

68.98 

Subtract : 


62.55 

(*) 

48.75 

00 

72.44 

49.8 

(J) 

85.3 

12.42 

25.30 

36.23 

37.5 

62.9 

Where  do  we  place  the  decimal  point  in  the  result  ? 

306.     1.     At  5^  each  how  many  oranges  can  I  buy 
for  .5  of  a  dollar? 

2.  A  farmer  who  had  100  sheep  sold  .1  of  them  to  a 
butcher  and  .5  of  them  to  a  drover.     How  many  did  he 
sell? 

3.  Mr.  Hall  gave  .3  of  $50  to  his  daughter  and  .7  of 
$50  to  his  son.     How  much  did  each  receive? 

4.  Clark  spent  $4,  which  was  .1  of  his  money.     How 
much  money  had  he? 

5.  If  $15  is  .3  of  my  cash,  what  is  .1  of  it? 

6.  From  2.2  take  .22.     From  4  take  .45. 

7.  Add  7.6,     7.8,     5.9,     3.4,     and    5.7. 

8.  Bertha  gave  .2  of  her  money  for  a  10-cent  doll. 
How  much  had  she  left? 


COMMON    FRACTIONS. 


209 


COMMON   FRACTIONS. 


0 


H 


307.    What  part  of  A  is  dark?    "What  part  is  light? 

Into  how  many  equal  parts  is  A  divided? 

Is  B  one  of  the  equal  parts  ?  What  part  of  the  rectangle 
isB? 

How  do  we  find  i  of  anything? 

How  does  the  line  CD  divide  the  rectangle  E?  What 
part  of  E  is  to  the  right  of  CD? 

What  part  of  this  half  is  H?    What  part  is  G? 

What  part  of  the  whole  rectangle  is  H?  Then  may  we 
find  i  of  a  thing  by  dividing  half  of  it  into  2  equal  parts? 

One-fourth  is  what  part  of  a  half?  How  many  fourths 
are  equal  to  a  half? 

What  is  2  times  i?    3  times  i?    4  times  i? 

How  many  times  must  I  take  i  to  make  f  ?    f  ?    -f-1 

What  part  of  E  are  Gr  and  H  together? 

One-half  of  A  is  how  many  times  i  of  it? 

What  part  of  A  is  B  +  O  +  M? 

How  many  fourths  of  E  is  J  of  it  +  i  of  it? 


o 

''///'•'S,                    -'/,'y''', 

H 

E 

A 

F 

308.     This  rectangle  is  divided  into 
Point  out  |  of  it,     f  of  it.     |  of  it. 

*i4 


equal  parts. 


210 


SCHOOL,    ARITHMETIC. 


How  many  eighths  of  it  are  dark?    How  many  are  light? 

How  many  fourths  of  it  are  dark?    How  many  are  light? 

One-eight  is  what  part  of  a  fourth?  How  many  eighths 
are  equal  to  i?  Tof?  To|? 

How  is  -J  obtained  from  i? 

What  is  2  times  -J?    3  times  i?    4  times  i?     6  times  £? 

How  many  eighths  are  there  in  the  rectangle?  How 
many  have  letters?  How  many  have  none?  f —  f  = 

How  many  fourths  of  the  rectangle  have  letters  ?  These 
3  fourths  are  equal  to  how  many  eighths  ?  f  =  ¥  ? 

What  part  of  the  whole  rectangle  is  H  +  A  +  E  +  F? 
How  many  fourths?  How  many  eighths?  f  =  -g- - 

Show  that  |  of  the  rectangle  =  f  or  |  of  it. 

What  part  of  the  rectangle  is  O?  What  part  is  D? 
What  part  is  O  +  D? 

What  is  -J  of  J  ?    i  is  equal  to  how  many  eighths  ?    J  ?   f  ? 

How  many  eighths  of  the  rectangle  is  i  of  it  +  -J  of  it? 

Six  quarters  are  worth  how  many  half  dollars?  f  are 
equal  to  how  many  halves? 


12 


309.  What  part  of  the  circle  is  shaded?  How  many 
thirds  of  it  are  not  shaded? 

The  dotted  line  divides  one  of  the  thirds  into  2  equal 
parts.  What  is  each  part  called? 


COMMON    FRACTIONS.  211 

One-sixth  is  what  part  of  one-third?  How  many  sixths 
are  equal  to  J?  To  f  ?  Tof? 

What  part  of  the  circle  is  below  EH?    Above  EH? 

Then  which  is  larger,  J  of  the  circle  or  J  of  it?  How 
much  larger? 

How  many  times  must  I  take  J  of  the  circle  to  make 
-f-  of  it?  To  make  the  whole  circle? 

What  part  of  the  rectangle  isA  +  B  +  C  +  D?  "Then 
C  +  D  is  what  part? 

What  part  of  the  rectangle  is  D  ?  Then  C  +  D  =  how 
many  twelfths?  i  of  •&  (or  |)  =  ^. 

How  many  ^y  s  are  there  in  the  rectangle  ?  In  £  of  the 
rectangle  ?  -J-  =  TT. 

What  part  of  the  rectangle  is  A  +  O  +  K? 

Which  is  larger,  i  of  the  rectangle  or  4  of  it?  Show 
how  much  larger. 

How  many  ^'s  of  the  rectangle  =  1  of  it  -f  ^  of  it  ? 

Find  how  many  -j^'s  of  the  rectangle  are  equal  to  f  of 
it.  To  f  of  it. 

Find  how  much  larger  i  of  the  rectangle  is  than  J  of  it. 

310.    Copy  and  complete: 


i 

:     T 

i 

r   z= 

"6T 

i=T*              f 

—     ¥ 

i 

¥ 

—     T 

i 

-   z^ 

-g- 

f  =TF              f 

=     ¥ 

i- 

—    T 

i 

r  = 

TF 

*=TF              * 

"6" 

1 

• 

2    -                              2 

T 

r  TT 

T 
< 

T2~ 

IT   "  TT               f 

~   TF 

311. 

What 

part 

of 

this 

rectangle 

is 

dark? 

How  many  fifths 

are  light  ? 

B     °   H 

How 

many  tenths 

of 

the 

rectangle 

E     D  " 

make  i 

of  it? 

One-half  of 

the 

dark 

portion  is  what  part  of 

the  whole 

figure?    £ofi  = 

212  SCHOOL    ARITHMETIC. 

What  part  of  the  figure  is  on  each  side  of  AH? 

Show  how  many  tenths  of  the  rectangle  make  |  of  it.. 

What  part  of  the  figure  is  E+B+C? 

If  D  were  removed,  what  part  of  the  whole  would 
remain? 

How  many  times  C+D  make  up  the  figure?  How  many 
times  J  =  1  ? 

How  many  fifths  of  a  nickel  make  a  dime  (two  nickels)  ? 
How  many  J's  in  2? 

Point  out  i  of  half  the  rectangle.  It  is  what  part  of 
the  whole?  J  of  \  = 

B+C+D+E  =  --  how  many  i's  of  the  figure?  How 
many^'s?  f  =  TT. 

How  many  -^'s  make  f  ?     f  ?     f  ?     |  ? 

How  many  y^'s  of  the  rectangle  =  -|-  of  it  +  y1^-  of  it? 

Which  is  larger,  f  of  the  rectangle  or  y3^  of  it?  How 
much  larger? 

Draw  a  10-inch  square  and  divide  it  into  square  inches. 

Each  small  square  is  what  part  of  the  whole? 

How  many  hundredths  in  the  upper  row?  Then  how 
many  hundredths  make  1  tenth? 

Find  how  many  hundredths  make  y3^,  or  ^.     y^,  or  ^. 

One-tenth  is  how  many  times  as  much  as  one-hundredth? 

Find  how  many  hundredths  in  i  of  the  large  square. 
In  f  of  it. 

One-hundredth  is  what  part  of  1  tenth? 

Point  out  y^j-  of  one-tenth  of  the  large  square,  and  tell 
what  it  is  called. 

Complete:     £=T  =^  =T  =T1F  =-^  ^ 
Complete:     l=f  =T  =T  = -$    =Tir  = 


COMMON    FRACTIONS.  213 

BCD 


312.  A,  B,  C,  and  D  are  equal  squares.  What  part  of 
each  is  dark?  Are  the  dark  parts  equal? 

Into  how  many  equal  parts  is  B  divided?  How  many 
of  the  dark  parts  are  equal  to  the  dark  part  of  A?  Then 
how  do  -J  and  i  compare  in  size? 

How  does  i  of  A  compare  in  size  with  -f  of  C?  Then 
what  can  you  say  of  ^  and  f  ? 

Compare  ^  of  A  with  -f  of  D,  and  state  what  you  learn. 

Are  2  of  the  equal  parts  of  B  equal  to  4  of  the  equal 
parts  of  D?  Is  |  greater  than  f  ?  Is  f  ? 

Arrange  the  fractions  J,  f ,  -J ,  and  J-  in  six  groups  of  two 
fractions  each.  Compare  each  two,  and  tell  what  you.  learn. 

In  the  fractions  £  and  -f-,  what  does  the  2  show  ?  The  1  ? 
The  8  ?  The  4  ? 

In  the  fraction  f ,  which  figure  indicates  the  number 
of  equal  parts  into  which  a  whole  is  divided?  What  shows 
us  how  many  of  the  parts  are  taken? 

The  number  below  the  line  of  a  fraction  shows  into  how 
many  equal  parts  anything  is  divided.  It  is  called  the 
Denominator. 

The  number  above  the  line  shows  how  many  of  the  parts 
are  taken.  It  is  called  the  Numerator. 

In  f  of  the  rectangle,  what  does  the  8  show  ?    The  5  ? 

Draw  on  the  board  a  line  4  ft.  long.  Measure  it  with 
your  foot  rule,  which  is  -J  yd.  in  length.  The  line  is  how 
many  thirds  of  a  yard  long? 


214  SCHOOL    ARITHMETIC; 

What  does  the  3  show?    What  does  the  4  show? 
Grive  the  meaning  of  the  numerator  and  of  the  denomi- 
nator in  f  .     In  f.  in.     In  f  yd.     In  £. 

313.    What  is  the  sum  of  a  quarter  and  a  half  dollar? 
The  half-dollar  =  2  quarters.     2  quarters  +  1  quarter  =  3  quarters. 

What  is  the  sum  of  4  bu.  and  a  peck? 

Add  J  gal.  and  i  gal.    4  +  i  =  T. 

Can  you  add  halves  and  fourths  without  changing  the 
halves  to  fourths? 

Use  your  foot-rule  to  find  the  sum  of  i  in.  and  i  in. 
To  find  the  sum  of  ^  in.  and  %  in. 

i  +  i  =  T-  f  +*==*• 

What  must  be  done  with  i  before  it  can  be  added  to 
i?  With  4? 

Only  like  numbers  can  be  added.    Fractions  to  be  added 

must  have  the  same  denominator. 

• 
314.    With  a  foot-rule  complete: 


.  =Tn.  n.--  n.  =¥n.  n.--  n.  =¥n. 
|  in.  -f|  in.  =-5-  in.  |  in.  +1  in.  =  F  in.  |in.+Jin.=-B-in. 
|  in.  -fi  in.  =¥  in.  \  in.  +|  in.  =¥  in.  f  in.  +|-  in.  =-g  in. 

When  one  fraction  is  to  be  subtracted  from  another,  both 
must  have  the  same  denominator. 


.  =-g-in.  -|in.  —  -Jin.  —  ^in.  1  in.  —  Jin.  =Tin. 
.  i=-g-in.  1  in.  —  -f-in.  =-§-in.  fin.  —  J-in.  =-g-in. 
in.  in.  —  in.  =in.  -in.  —  -in.  =-in. 


COMMON    FRACTIONS.  215 

315.     Find  the  value  of: 


3  +i— i 

T  T  T  f  ~T  ¥  ~T   g-  "2  i  f+t  T 


3 
T 

f  + 


'+  i  +  i       I  - 


316.     Copy  and  complete: 

2  times  J  =  J  or  J.  3  X  f  =  -g-  or  T. 

2  times  |  =  f  or  T.  2  X  f  =  -g-  or  T. 

2  times  i  =  T  or  T.  4  X  f  =  T  or  T. 

2  times  f  =  -g-  or  -g-.  8  X  -g-  =  -§-  or 
4  times 


317.  How  many  |'s  =  -J-?  How  many  |'s  =  -J-? 
|-  r=  how  many  times  ^  ?  |-  =  how  many  times  ^-  < 
How  many  times  is  1  ft.  contained  in  3  ft  ? 

3  ft.  -=-  1  ft.  =  -  .      3  fourths  -f-  1  fourth  =  - 


6  yd.  -T-  2  yd.  = times,      f  -f-  f  — times. 

i  of  2  qt.   =  -      -  qt.  t  of  J  =  T. 

1.  of  3  ft.    -  ft.  tof|  =  T. 

i  is  contained  in  i  -    —  times, 

i  is  contained  in  i  — -  -  times. 

i  is  contained  in  \  how  many  times? 

i  is  contained  in  f  how  many  times? 

f  is  contained  in  -J  how  many  times? 

f  is  contained  in  f  how  many  times? 

i  is  contained  in  1  how  many  times? 
J  is  contained  in  2  how  many  times? 


216  SCHOOL    ARITHMETIC. 

How  many  J's  are  there  in  1?     In  2?     In     5? 
How  many  £'s  are  there  in  2?     In  5?     In  12? 
How  many  -J's  are  there  in  1?     In  2?     In  3? 
How  many  eighths  of  an  inch  in  4  inches?  In  12  inches? 

318.  Complete  and  read: 

1  in.   +  |  in.  =  14  in.   (one  and  one-half  inches),  or 
ir  m- 

2  in.   +  i  in.  =  3  in.   +  f  in.  = 
1  in.   +  4  in.  =                      1  hr.  +  f  hr.  - 
5  in.  +  f  in.  =                     4  gal.  +  J  gal.  = 

319.  In  1|  gal.  how  many  fourths?    How  many  quarts? 
In  2J  bu.  how  many  halves?    How  many  pecks? 

In  1-J  in.  how  many  eighths?    In  2-J  inches? 

In  $3f  how  many  fourths,  or  quarters? 

In  2^  yd.  how  many  halves?    How  many  fourths? 

Change  to  fourths : 

•  i       n       4*       i       if       v- 

H         3i  I.        I         si         V 

Six  half -inches  =  how  many  inches? 

Twelve  quarter-inches  =  how  many  inches? 

Three  half  inches  =  how  many  inches  and  half -inches? 

How  many  inches  in  f  in.?     In  |  in.?     In  ±f-  in.? 

How  many  inches  and  half -inches  in  f  in.?     In  %  in.? 

320.  1.     If  a  horse  eats  three  times  a  day;  and  eats 
2  pk.  of  oats  at  a  time,  how  many  half -pecks  will  he  eat 
in  6  days?    How  many  pecks?     How  many  bushels? 

2.     When  milk  is  3^  a  pint,  how  much  must  be  paid 
for  li  quarts? 


COMMON    FRACTIONS. 


217 


3.  If  \  of  a  yard  of  cloth  costs  24^,  what  does  \  of  a 
cost? 

4.  How  many  sheets  of  paper  at  J#  apiece  can  you 
buy  for  5^? 

5.  If  |  of  a  yard  of  ribbon  costs  18#,  what  is  the  cost 
of  1  of  a  yard?     Of  J  of  a  yard? 

6.  Tom  earned  i  of  a  dollar  on  Monday  and  J  of  a 
dollar  on  Tuesday.     How  much  did  he  earn? 

7.  A  box  is  |  yd.  long  and  -J  yd.  wide.     By  how  much 
does  the  length  exceed  the  width? 

8.  Each  side  of  a  square  is  f  ft.  long.     What  is  the 
perimeter? 

9.  A  lady  who  had  J  of  a  gallon  of  milk  sold  a  quart 
to  a  neighbor.    What  part  of  a  gallon  had  she  left? 

10.  A  man  who  had  $40  spent  $10.     What  part  of  his 
money  had  he  left? 

11.  Tillie  had  f  of  a  yard  of  velvet  and  gave  Nell  J 
of  it.    What  part  of  a  yard  had  Tillie  left? 

12.  Draw  a  rectangle  12  in.  long  and  i  as  wide-    How 
many  square  inches  in  \  of  it?    In  j  of  it? 


Common  Denominator. 

A  B  C 


321.  How  many  J's  are  eqiial  to  4?  Then  -J  is  how 
many  times  \\ 

Multiply  numerator  and  denominator  of  -J  by  2.  What 
is  the  result? 

When  4  is  changed  to  f,  how  is  the  size  of  the  parts 
changed?  Are  more  of  them  taken? 


218  SCHOOL    ARITHMETIC. 

By  what  must  numerator  and  denominator  of  i  be 
multiplied  to  change  it  to  -f- 1 

The  part  on  the  left  of  CD  is  how  many  times  as  large 
as  one  of  the  parts  on  the  right? 

The  number  of  parts  on  the  right  of  CD  is  -  -  times 
the  number  of  parts  on  the  left. 

Multiply  numerator  and  denominator  of  i  by  3,  and 
explain  the  result. 

Divide  numerator  and  denominator  of  f  by  4.  Is  the 
result  equal  to  -|  3 

By  what  must  you  divide  numerator  and  denominator 
of  T5Q-  to  change  it  to  \\ 

Show  that  the  following  is  true: 

If  both  numerator  and  denominator  of  a  fraction  are 
multiplied,  or  divided,  by  the  same  number,  the  value  of 
the  fraction  is  not  changed. 

322.    Change  i?    J,    and  f  to  12ths. 

Both  numerator  and  denominator  of  i  must  be  multi- 
plied by  12  -f-  2,  or  6. 

Both  numerator  and  denominator  of  f  must  be  multi- 
plied by  12-S-3,  or  4. 

By  what  must  both  numerator  and  denominator  of  f  be 
multiplied? 

Change : 

1.  £,    •£,  and  £  to  12ths. 

2.  i,    f ,  and  £  to  8ths. 

3.  i,   f,  and  ^  to  lOths. 
4      £?    |?  |5  and  |  to  12ths. 
5*.     i,   I,  i,  and  ^  to  20ths. 

6.  t,   |,   i,  and  ^  to  40ths. 

7.  |,   t,   f,  and  TV  to  lOOths. 

8.  f,  A,  «,  and  ^  to  4ths. 


COMMON    FRACTIONS.  219 

323.  Change  to  smaller  denominators: 

9.   f,  f,  TW?  12.    A.M.-H.M- 

•in         466          8  10          102040 

-LU-        65    8'    10'   T2  *«>•        25'    30'   ~5"0~' 

11-      t,  TV  ii,  H  I*-      T¥«,  TV 

15.  In  ^  of  a  dozen  how  many  half  dozen? 

16.  In  f  of  a  dozen  how  many  y^'s  of  a  dozen? 

17.  In  -J-  of  a- dozen  how  many  y^'s  of  a  dozen? 

18.  How  many  more  oranges  are  ^  of  a  dozen  than  ^  of 
a  dozen  ?     What  part  of  a  dozen  more  ? 

19.  How  many  12ths  of  a  foot  (inches)  in  ^  foot?     In 
|  foot  ? 

20.  In  1-J-  yards  how  many  thirds  ?    How  many  feet  ? 

21.  How  many  yards  in  f  yd.  ?     How  many  feet  ? 

22.  How  many  ones  are  equal  to  -§-  ?     -^2-  ?     T|-  ? 

23.  How  many  ones  and  thirds  in  JJ     In  -J?     ^-? 

24.  In  f  how  many  fourths  ?     In  J  how  many  halves  ? 

25.  Change  1^  bu.  and  J  bu.  to  pecks,  or  fourths  (of  a 
bushel). 

Addition  and  Subtraction. 

324.  Fractions  that  have  a  common  denominator  are 
called  Similar  fractions.      Only  similar  fractions  can  be 
added  or  subtracted.     Change  to  similar  fractions  and  add 
or  subtract  as  indicated: 

1-    *+  i  =  e  9-   f +A=T7        17.     t  -  -  i  =  ¥ 

2.   *+i=ir          10.   i+TV=T2        18-     t--i=T 

3-  H-i=T          11.   i+A=n        19-    i  -  -  t  =  T 

4-  *+i==lT  12-     1+TV=TT  20.      i--TV=T2 

5.  *+*  =  T  13.     t+A=TT  21.      f--A=TT 

6.  *+t-T  14.    i+A=TT          22.      |--TV=TT 

7-   i+A=T^         16.   t+*=TT        23.   A--i=n 

8.          =         ie---=         24.      --= 


30. 

i+i+- 

ro 

35. 

1         -A 

31. 

1+1+ 

\ 

36. 

7                  2 
TTF              5 

32. 

1+1+ 

i 

37. 

i          -    i 

33. 

i+t+ 

! 

38. 

i       -  i 

34. 

A+i  +  : 

r¥o 

39. 

l^-T50 

220  SCHOOL    ARITHMETIC. 

Find  the  value  of: 

25. 
26. 
27. 
28. 
29. 

In  the  following  exercises  add  the  integers  and  frac 
tions  separately,  and  then  add  the  results: 

40.  3f    +  7|  45.      6i  +  2|    +    1£ 

41.  2i    +  5|  46.      9|  +  3£    + 

42.  6|    +  3i  47.      8£  +  7^  + 

43.  i|    _j_  45  48.      2f  +  5T77  + 

44.  8^5-  +  5|  49.  10£  +  9|    +  26Tyo 

50.    Subtract  2f  from  5^. 

5 if  =  ^T  :      ^T       The  fractions  are  first  made  similar.     We  can- 

2J  =  2 J  =  2J    not  take  f  from  f ,  so  we  take  1  one,  or  f ,  from 

the  5  ones,  and  add  it  to  the  f .     We  then  take  f 

c\  Q  O  ^ 

^4:  *T    from  f ,  and  2  from  4. 

Subtract : 

51.  1%  from  10^  56.  12J-      from  16J 

52.  3|  from    6£  57.  22^      from  30| 

53.  Sffrom    9J  58.  31f      from  42£ 

54.  2ifrom    7|  59.  16T7o     from  2 Of 

55.  4f  from    8^  60.  37-^-  from  62^ 


COMMON    FRACTIONS.  221 

Multiplication  and  Division. 
.325.     Complete: 

3  times  -i-  =  -g-  or  T  2  X  TV  =  TT  O1*  ^ 

2  times  ^-  =  g-  or  ^  3  X  yV  ~  T2  or  T 

2  times  f  =  ¥  or  3-  -i  X  -^  —  T2  or  ^ 

3  times  -|  =  -g-  or  6  X  yV  =  TT  or  2" 
3  times  ^  =  ^  or  8  X  -^  —  TT  or  3- 
1  times  -|  —  -g-  or  9  X  -^  —  T T  or  T 
6  times  -J-  =  -g-  or  6  X  -£%  =  TT  or 

326.     How  many  -i-'s  =  -J-?     How  many  y^-'s  =  -J? 
-|  —  how  many  times  -J-?     |-  :=  how  many  -J-'s?     iV'8^ 
How  maii^  times  is  1  contained  in  |-,  or  4-  ? 

t/  b  b " 

3  sixths  -r-  1  sixth  = times,     f  -r-  -g-  = times. 

^  is  contained  in  -J times.     -J-  -j-  ^-  = 

jr  is  contained  in  1 times.      1  -=-  ^  = 

y^-  is  contained  in  ^ times.     ^  -f-  ^  =: 

y^  is  contained  in  -J- times.     -J-  -f-  TV  = 

^  of  2  sixths  —  -s-.       i  of  -I  =---. 

b  -  b  b 

i  °f    f    =   IT"          i  °f    A   =    TT  01*  -6 ' 

-1     OT      ~      JL     syr          6          „___    OT*    

How  many  ^'s  are  there  inl?     In  2?     In  4? 
How  many  -J-'s  are  there  in  1  ?     In  2  ?     In  5  1 
How  many  y^-'s  are  there  in  1  \     In  2  ?     In.  3  \ 
How  many  y^'s  of  a  foot  in  2  inches  ?     In  6  inches  ? 
Four  inches  is  what  part  of  a  foot  \ 
How  many  inches  =  f  of  a  foot  ?     f  of  a  foot  \ 


222 


SCHOOL    ARITHMETIC. 


327.  If  each  third  of  A  is  divided  into  2  equal  parts, 
as  in  B,  how  many  parts  will  there  be? 

What  is  each  part  of  B  called?    -J  of  -J  =-g. 

How  many  fifths  of  E  are  there  to  the  left  of  CD? 

How  many  thirds  of  this  part  of  E  are  dark? 

How  many  fifteenths  of  E  are  dark  ? 

Thenfof  f==Tir.     tXf  = 

In  finding  f  of  f  how  was  the  15  obtained?  How  was 
the  numerator  obtained? 

To  multiply  one  fraction  by  another — 

We  take  the  product  of  the  numerators  for  the  required 
numerator,  and  of  the  denominators  for  the  denominator. 


Find  the  product  of: 


1. 

f  X  f 

7. 

2. 

J  x  i 

8. 

3. 

f  x  i 

9. 

4. 

fx  1 

10. 

5. 

*x| 

11. 

6. 

t.x  4 

12. 

i  x  I  x  ! 
i  x  1  X  | 
I  x  t  x  f 
I  x  t  x  i 

f  X  f  Xf 

4  x  I  x^ 


13. 
14. 
15. 
16. 
17. 


x  ! 


t  x 
tx 
f  x 


COMMON    FRACTIONS.  223 


19.  Multiply  34  by  6. 

34 
6 


18     =  6  X   3  We  multiply  the  integral  part,  then  the 

3     =0^1          fractional,  and  add  the  results. 

21       =  6  X   34 
Find  the  products: 


20. 

6 

X 

44 

25. 

7 

X  6f 

30. 

4 

X 

124 

21. 

9 

X 

H 

26. 

4 

X  5| 

31. 

6 

X 

374 

22. 

5 

X 

^ 

27. 

8 

v  3  5 

/\   ""J" 

32. 

6 

X 

16| 

23. 

4 

X 

3* 

28. 

6 

v  4  ^ 

33. 

3 

X 

33£ 

24. 

3 

X 

9| 

29. 

9 

X  Tf 

34. 

8 

X 

624 

328,     1.     Divide  4  ft.  by  2  ft.   4  thirds  by  2  thirds. 

2.  Find  4  of  4  thirds.     -f  -=-  2  =  f . 

3.  How  many  f 's  in  f  ?     -|  -=-  f  = times. 

Find  the  quotients: 

4.  |   -j-  2  9.     -J  -T-  f          14.     I  -T-  TV 

5.  |   -  3  10.     f  -  |          15.     4  -  yV 

6.  A  -5  11.     I-  I          16.     I-  A 

7.  1-4          12.     |  -  f          17.     4  -=-   l 

8.  TV  -7-2          13.     |  -  I          18.     |  -   f 

19.     Write  these  fractions  in  a  line,  placing  the  largest 

first,  the  next  largest  second,  and  so  on:  J,  4?  47  4?  yV? 
i      i      i    A    3      i 

T>  TS~5  "S"'    85  T'  TFO"' 


224 


SCHOOL    ARITHMETIC. 


What  does  it  contain  -J, 


329.  How  many  sixths  of  A  are  shaded?     How  many 
times  is  f-  contained  in  A  \     Can  you  find  out  by  inverting  -|  \ 

Find  how  many  times  A  contains  •£  (the  light  part). 
What  does  A  contain  6  times  ? 
or  2  times? 

B  contains  -J  how  many  times  ?     Can  you  tell  by  invert- 

ing  I? 

Invert  -|  and  show  how  many  times  it  is  contained  in  the 
whole  of  B. 

In  B,  I-  is  contained  2f  times,  or  4  times. 

'     o  *->  o 

Can  we  find  how  many  times  a  fraction  is  contained  in  a 
whole  or  1  by  inverting  the  fraction  '{ 

Find  how  many  times  1  contains  i,  i,  -J,  f  ,  T5T,  f  . 

One-half  is  contained  in  one,  2  times;  in  four  it  is  con- 
tained -  —  times. 

How  many  times  is  \  contained  in  1?  In  2?  In  5? 
In  I? 

To  divide  by  a  fraction  — 

Multiply  the  inverted  divisor  l)y  the  dividend. 

330.  1.     Divide  4  by  f. 

I  =  the  number  of  f's  in  1. 
4X1  =  -VS  or  6,  the  number  of  f's  in  4. 


Divide  : 

2. 

5  b; 

7  i 

8. 

6 

by  1 

14. 

10 

by 

f 

3. 

3b; 

Y  \ 

9. 

2 

by  f 

15. 

3 

by 

i 

4. 

6b; 

n 

10. 

5 

by  I 

16. 

2 

by 

1 

5. 

4b; 

Y  i 

11. 

8 

by  I 

17. 

5 

by 

A 

6. 

7b 

y  i 

12. 

3 

by  I 

18. 

4 

by 

1 

7. 

5  b; 

7  -nr 

13. 

4 

by  A 

19. 

2 

by 

9 
TTT 

COMMON    FRACTIONS.  225 

20.     Divide  J  by  §. 

Inverted  divisor  f  =  the  number  of  f's  in  1. 
f  X  I  =  I,  or  1$,  the  number  of  f's  in  f . 

Find  the  quotients: 

21.  |  -*•  i         25.     *  -  TV  29.  |  -4-    i 

22.  i  -=-  f        26.     |  -   i  30.  |  ^   f 

23.  i-i        27.     f-*-   *  31.  4-5-   | 

24.  i  -  i        28-1-1  32.  |  -s-  'A 

331.      1.     Ella  picked  i  gal.  berries  and  Nora  picked  f 
gal.     They  both  picked gal. 

2.  What  is  the  difference  between  J  of  an  hour  and 
J  of  an  hour? 

3.  How  much  will  3^  quarts  of  milk  cost,  if  1  pint 
is  worth  3  cents? 

4.  If  carpet  is  f  yd.  wide,  how  wide  a  room  will  6 
widths  cover? 

5.  If  i  of  a  yard  of  ribbon  costs  2$,  how  many  yards 
can  you  buy  for  32  cents? 

6.  If  I  had  J  of  a  yard  of  ribbon,  and  used  i  of  a  yard, 
what  part  of  a  yard  have  I  left? 

7.  At  y^Q-  of  a  dollar  a  peck,  how  many  pecks  of  apples 
can  be  bought  for  $f  ?     For  $1? 

8.  If  a  boy  earns  $|  a  day,  in  12  days  he  will  earn 

9.  How  many  127s  of  a  foot  are  equal  to  a  yard? 

10.  At  i  of  a  dollar  a  pound,  how  many  pounds  of 
coffee  can  I  buy  for  $1?    For  $5? 

11.  James  sold  2  bushels  of  apples  at  10^  a  half -peck. 
How  much  did  he  get  for  them? 

*i5 


226  SCHOOL    ARITHMETIC. 

12.  4  horses  are  J  of  -      -  horses.     (Show  by  dots.) 

13.  One-third  of    12    sheep  is  -      -  sheep."     f  of  12 
sheep  are sheep. 

14.  8  quarts  are  §  of  how  many  quarts?     (Show  by 
dots  or  squares.) 

15.  Bell  bought  a  book  for  10^,  which  was  i  of  her 
money.     How  much  had  she? 

16.  There  are  36  gallons  of  cider  in  a  barrel  which  is 
f  full.     How  many  gallons  will  the  barrel  hold? 

17.  A  3-gallon  pail  was  full  of  water,  but  2  quarts  were 
taken  out.     What  part  of  the  water  was  taken  out?  What 
part  was  left? 

18.  If  f  of  a  yard  of  cloth  cost  15^,  what  is  the  cost  of 

1  of  a  yard?     Of  1  yard?     Of  2  yards? 

19.  If  T3F  of  the  cost  of  a  wagon  was  $12,  what  was 
the  entire  cost? 

20.  If  -i  bu.  of  corn  is  worth  20^,  what  is  the  value  of 

2  bushels?    Of  2i  bu.? 

21.  Adam's  house  is  f  of  a  mile  south  of  the  school- 
house,  and  Dick's  is  f  of  a  mile  north,     How  far  apart  do 
the  boys  live? 

22.  In  a  school  of  48  scholars  f  are  girls.     How  many 
boys  are  there? 

23.  If  \  lb.  of  coffee  costs  $.15,  what  will  2  pounds 
cost? 

24.  How  many  pieces  of  velvet,  each  half  a  yard  long, 
can  be  cut  from  a  piece  9J  yards  long? 

25.  I  have  a  jointed  fishing  rod  in  3  parts.     One  part 
is  2J  feet  long,  another  2f  feet,  and  the  other  3}  feet. 
How  long  is  the  rod? 

26.  f  of  the  days  in  April  are  how  many  days? 


RELATIONS RATIO.  227 

27.  From  a  piece  of  ribbon  J  ft.  long  a  piece   -f^  ft. 
long  was  cut  off.     Show  the  length  of  the  remainder. 

28.  A  rectangle  is  i  ft.  long  and  i  ft.  wide.     What  is 
the  perimeter?    How  many  square  inches  does  it  contain? 

29.  A  box  is  li  ft.  long  and  f  ft.  wide.     Find  how 
many  square  inches  in  the  lid. 

30.  A  lady  bought  3j  yd.  of  ribbon,  and  divided  it 
equally  among  5  girls.     What  part  of  a  yard  did  each  girl 
get?     (3J  yd.  -f-  5  =  -1/  Jd-  +  5)- 

31.  Draw  an  8-inch  square.     In  it  draw  a  square  i 
as  large.     How  many  square    inches    between    the    two 
perimeters  ? 

Relations— Ratio. 

332.  1.  One  line  is  12  ft.  long,  another  is  3  ft.  long. 
Compare  their  lengths. 

(a]  The  3-ft.  line  must  be  taken  (repeated) times  to  make 

up  the  12-ft.  line. 
(6)  The  12-ft.  line  is times  as  long  as  the  3-ft.  line. 

(c)  The  12-ft.  line  is  composed  of 3-ft.  lines. 

(d)  The    3-ft.  line  is  one  — —  as  long  as  the  12-ft.  line. 

By  comparing  or  measuring  we  find  the  answers  required.  When 
we  know  the  answers  to  a  and  fc,  we  know  the  relation  (ratio]  of  12 
ft.  to  3  ft.  The  ratio  is  4. 

When  we  know  the  answers  to  c  and  d,  we  know  the  ratio  of  3  ft. 
to  12  ft.  It  is  J. 

2.  One  package  weighs  2  lb.,  another  8  Ib.    Make  four 
statements  similar  to  the  four  above,  and  find  the  ratio  of 
each  weight  to  the  other. 

3.  Measure  your  foot-rule  with  a  4-inch  unit.      Tell 
what  you  can  about  the  ratios. 

4.  Find  the  ratio  of  your  foot-rule  to  a  6-inch  unit. 
A  2-inch  unit.     A  1-inch  unit. 


228  SCHOOL    ARITHMETIC. 

5.  What  is  the  ratio  of  the  6-inch  unit  to  the  foot-rule? 
Of  the  2-inch  unit?     The  1-inch  unit? 

6.  Find  two  ratios  by  comparing  a  yardstick  and  a 
foot-rule. 

7.  What   two   ratios   can  be  found  by  comparing  a 
gallon  and  a  quart? 

8.  Draw  a  2-in.  square  and  a 
4-in.    square.      Divide    them    into 
square  inches,  and  find  the  ratio  of 
each  to  the  other. 

9.  What  is  the  ratio  of  a  dollar 
to  a  dime?    Of  a  dime  to  a  dollar? 

10.  Ten  is  how  many  times  2?    Then  what  is  the  ratio 
of  10  to  2?     Of  2  to  10? 

11.  How  many  times  must  one  be  taken  to  make  ten? 

Then  the  ratio  of  10  to  1  is  ,  and  the  ratio  of  1  to 

10  is  -    — . 

12.  The  ratio  of  10^  to  -    —  tf  is  2.    The  ratio  of  -    —j 
to  10#  is  J. 

13.  A  man  counting  a  roll  of  5-dollar  bills  says,  $5, 
$10,  $15,  $20.    How  many  equal  parts  make  up  his  $20? 
How  many  times  must  one  of  the  parts  be  taken  to  equal 
his  $20?    What  is  the  ratio  of  $20  to  $5?    Of  $5  to  $20? 

14.  $50  is  how  many  times  $10?    That  is,  what  is  the 
ratio  of  $50  to  $10? 

15.  Four  feet  is  what  part  of  20  feet?    That  is,  what 
is  the  ratio  of  4  ft.  to  20  ft? 

16.  Five  inches  is  one-half  of  what?    That  is,  the  ratio 
of  5  in.  to in.  is  -J. 

17.  Thirty  dollars  is  five  times  what?     That  is,  the 
ratio  of  $30  to  $ is  5. 


RELATIONS RATIO.  229 

18.  What  is  the  ratio  of  i  (f )  to  |  ?     Of  £  to  £  ?     Of 
•|-  to  ^  ?     Show  by  drawing. 

19.  Find  the  ratio  of  24  to  8.     Of  42  to  6. 

20.  By  what  process  do  you  find  the  ratio  of  one  num- 
ber to  another?    (See  Division.) 

21.  Select  any  number  you  please,  and  state  its  ratio 
to  one.     To  two. 

333, 

ARTICLE  COST  ARTICLE  COST 

1  apple       2  cents  2  apples     5  cents 

5  apples  10  cents  8  apples  20  cents 

Five  apples  are  how  many  times  1  apple?  Then  they 
will  cost  how  many  times  as  much?  Point  out  two  ratios 
that  are  equal.  Eight  apples  are  how  many  times  2  apples  ? 
How  many  times  as  much  will  they  cost?  Point  out  the 
ratios. 

1.  At  3^  each,  what  will  be  the  cost  of  a  dozen  oranges? 
.  2.  When  lemons  are  selling  at  the  rate  of  3  for  5#, 
what  will  a  dozen  cost? 

3.  If  11  lb.  of  sugar  cost  50^,  what  will  22  Ib.  cost? 

4.  When  you  can  buy  3  handkerchiefs  for  25^,  how 
many  can  you  buy  for  $1? 

5.  A  lady  paid  30^  for  a  dozen  eggs.   How  much  would 
4  eggs  cost  at  that  rate? 

6.  A  boy  running  takes  3  steps  every  10  ft.     How 
many  steps  does  he  take  in  miming  100  ft.? 

7.  A  man  earns  $21   every  two  weeks.     How  much 
does  he  earn  in  six  weeks? 

8.  How  much  do  I  gain  by  buying  10  pigs  at  $2  each, 
and  selling  them  at  $3  each? 

(a)  How  much  do  I  gain  on  1  pig?    On  10? 

(b)  How  much  do  I  pay  for  the  10  pigs?    How  much  do  I  get 

for  them  ?    Then  how  much  do  I  gain  ? 


230  SCHOOL    ARITHMETIC. 

9.  If  5  apples  cost  10  cents,  what  is  the  cost  of  1  apple? 

10.  If  4  sheep  are  worth  $20,  what  are  3  sheep  worth?. 

11.  A  girl  bought  3  pairs  of  shoes  for  $6.     At  the 
same  rate,  what  would  5  pairs  cost? 

12.  Draw  two  lines  showing  the  ratios  4  and  \. 

13.  What  is  the  ratio  of  a  rectangle  4  in.  by  5  in.  to 
one  2  in.  by  5  in.? 

Review. 

334.     1.     Find  the  cost  of  a  ton  of  hay,  when  f  of  a 
ton  costs  $6. 

2.  9  is  f  of  what  number? 

3.  15  is  f  of  what  number? 

4.  14  is  f  of  what  number? 

5.  20  is  -|  of  what  number? 

6.  3J  is  f  of  what  number? 

7.  If  |  of  a  yard  of  satin  costs  80^,  what  is  the  cost 
of  one  yard?     Of  5  yards? 

8.  If  |  of  a  ton  of  coal  occupies  24  cubic  feet,  how 
many  cubic  feet  will  1  ton  occupy? 

9.  If  f  of  a  barrel  of  fish  cost  $10,  what  will  1  barrel 
cost? 

10.  What  is  the  price  of  a  dozen,  when  f  of  a  dozen 
oranges  sell  for  20^? 

11.  2  times  f  are  how  many  fourths? 

12.  i  of  18  is  i  of  what  number? 

13.  If  f  of  a  pound  of  rice  costs  6  cents,  what  will  5 
pounds  cost? 

14.  What  is  the  cost  of  6i  gallons  of  molasses  at  $.40 
a  gallon? 

15.  A  woman  has  15  yards  of  muslin.    How  much  will 
she  have  after  she  uses  14|  yards? 

16.  What  is  the  cost  of  §  of  a  pound  of  candy  at 
a  pound? 


REVIEW.  231 

17.  What  will  15i  dozen  eggs  cost  at  20^  a  dozen? 

18.  A  boy  after  selling  -J  and  i  of  his  marbles  had  12 
marbles  left.     How  many  had  he  at  first? 

19.  A  boy  has  £  of  a  peck  of  nuts.     If  he  gives  away 
|  of  them,  what  part  of  a  peck  will  he  have  left? 

20.  If  i  of  an  ounce  of  tea  costs  5^,  what  will  1  pound 
cost? 

21.  Four  fifths  of  20  is  f  of  what  number? 

22.  If  I  can  buy  7  pencils  for  -£$•  of  a  dollar,  how  many 
can  I  buy  for  -f^  of  a  dollar? 

23.  If  |  of  a  cord  of  wood  is  sold  for  $4,  what  will  5 
cords  bring? 

24.  If  f  of  a  barrel  of  sugar  costs  $12,  what  will  f 
of  a  barrel  cost? 

25.  If  y1^  of  a  lot  of  goods  is  worth  $360,  what  is  4 
of  the  lot  .worth? 

26.  $40  is  equal  to  i  of  my  house  rent  for  1  year.  How 
much  do  I  pay  a  month? 

27.  If  -J  of  a  ton  of  coal  lasts  2  days,  how  long  will  J 
of  a  ton  last? 

28.  What  will  J  of  a  pound  of  tea  cost  at  f  of  a  dollar 
a  pound? 

29.  At  i  of  a  dollar  a  bushel,  how  many  bushels  of 
apples  can  be  bought  for  10  dollars? 

30.  One  third  of  a  pole  is  blue,  J  of  it  is  red,  and  the 
rest  is  white.     What  part  of  the  pole  is  white? 

31.  If  5i  pounds  of  nuts  are  divided  equally  among 
7  boys,  what  part  of  a  pound  will  each  boy  receive? 

32.  When  a  furnace  consumes  coal  at  the  rate  of  f  of 
a  ton  a  day,  how  much  will  it  consume  in  4-|  weeks? 

33.  When  f  of  a  yard  of  ribbon  is  put  into  a  loop,  how 
many  loops  can  be  made  from  3  yards? 

34.  At  f  of  a  cent  a  square  foot,  what  will  it  cost  to 
paint  a  blackboard  24  feet  long  and  4|  feet  wide? 


COMPOUND    NUMBERS.  233 

COMPOUND    NUMBERS. 

Liquid  Measure. 

335.    Liquid  Measure  is  used  in  measuring  liquids,  as 
water,  milk,  etc. 


PINT  QUART  GALLON 

2  pints  (pt.)  =  1  quart  (qt.). 
4  quarts          =  1  gallon  (gal.). 

1.  How  many  pints  are  there  in  3  qt.?     In  5  qt.? 

2.  How  many  quarts  are  there  in  3  .gal.?    In  10  gal.? 

3.  How  many  pints  in  5  gal.  3  qt.  and  1  pt.? 
5  gal.  =5X4  qt.,  or  20  qt. ;  20  qt.  +  3  qt.  =  23  qt. 
23  qt.  =  23  X  2  pt.,  or  46  pt.;  46  pt.  -f   1  pt.  =  47  pt. 

4.  How  many  pints  in  4  gal.  2  qt.  1  pt.? 

5.  How  many  gallons  are  there  in  24  qt.?    In  40  qt. ? 

6.  How  many  quarts  are  there  in  12  pt.?     In  16  pt.? 

7.  How  many  gallons  are  there  in  110  pints? 

1  pt.  —  £  of  a  qt.,  and  110  pt.  =  110  X  $  qt.,  or  55  qt. 

1  qt.  =  \  of  a  gal.,  and  55  qt.  =  55  X  i  gal.,  or  13  gal.  and  3  qt. 

8.  How  many  gallons  in  129  pints? 

9.  How  many  pints  in  1  gal.  ?    In  -J  gal.  ? 

10.  How  many  gallons  in  40  quarts?     In  75  qt.? 

336.  1.  How  many  quart  jars  will  hold  2-J  gallons 
of  milk? 

2.  How  many  half-pint  bottles  can  you  fill  with  a 
gallon  of  olive  oil? 


234 


SCHOOL    ARITHMETIC. 


3.  A  milkman  sold  18  gal.  of  milk  at  6^  a  qtfart.    How 
much  did  he  get  for  it? 

4.  At  10^  a  pint,  how  much  syrup  can  be  bought  for 
$3.60? 

5.  How  many  pint  bottles  will  hold  2  gal.  1  qt.  of  oil? 

6.  If  a  gallon  of  molasses  costs  80^,  how  much  will  6 
pints  cost? 

7.  A  man  bought  2  cans  of  mineral  water,  each  con- 
taining a  gallon  and  a  half.     The  price  was  20^  a  gallon. 
How  much  did  he  pay? 

8.  There  are  231  cu.  in.  in  a  gallon.     How  many  cubic 
inches  in  a  quart? 

9.  A  lady  sold  2  gal.  3  qt.  1  pt.  of  vinegar  at  6#  a 
quart.     How  much  did  she  get  for  it? 

10.  A  man  paid  52^  for  1  gal.  2  qt.  1  pt.  of  milk.    He 
paid  -    — #  a  quart. 

11.  If  a  family  pays  8^  a  quart  for  milk  and  uses  3 
pt.  a  day,  what  is  the  milk  bill  for  the  month  of  March? 

12.  If  a  barrel  holds  31-|  gallons,  and  a  hogshead  holds 
twice  as  much,  what  does  a  hogshead  hold? 

Dry  Measure. 

337.    Dry  Measure  is  used  in  measuring  dry  articles, 
as  grain,  seeds,  fruit,  vegetables. 


UP 

PINT 


QUART 


PECK 

2  pints  (pt.)  =  1  quart  (qt.). 
8  quarts  =  1  peck  (pk.). 
4  pecks  =  1  bushel  (bu.). 


BUSHEL 


COMPOUND    NUMBERS.  235 

1.  How  many  pints  in  3  qt.?     In  5  qt.? 

2.  How  many  qt.  in  4  pk.  ?     In  5  pk.  ? 

3.  How  many  pk.  in  3  bu.?     In  7  bu.? 

4.  How  many  quarts  in  5  bu.  3  pk.  4  qt.? 

5.  How  many  pecks  in  8  bu.  3  pk.? 

6.  How  many  pecks  in  32  qt.  ?     In  20  qt.  ? 

7.  How  many  bushels  in  4096  pints? 

8.  How  many  pecks  in  J  bu. ?    In  i  bu.? 

9.  In  32i  pecks  how  many  bushels? 
10.  In  784  quarts  how  many  bushels? 

338.     1.     When  potatoes  are  worth  80^  a  bushel,  what 
is  i  peck  worth? 

2.  If    apples    are    selling  at  10^  a  quarter-peck,  how 
much  will  a  bushel  cost? 

3.  A  boy  sold  -J  bu.  of  berries  at  5^  a  quart.     He 
received  -     — #  for  them. 

4.  Two  bushels  of  cherries  were  divided  equally  among 
4  persons.     How  many  quarts  did  each  receive? 

5.  A  man  bought  5  bu.  3  pk.  of  corn  at  40^  a  bushel. 
How  much  did  it  cost  him? 

6.  How  many  peck  baskets  can  you  fill  with  64  qt. 
of  onions? 

7.  A  woman  bought  2  bu.  1  pk.  3  qt.  of  strawberries 
at  5^  a  quart.     She  paid  for  them  with  a  $5-bill,  and  got 
$ —    -  in  change. 

8.  How    many    pint    packages  can  a  seedsman  make 
from  2  bu.  2  pk.  and  2  qt.  of  seeds? 

9.  A  grocer  bought  10^  bu.  of  apples  at  60^  a  bushel, 
and  sold  them  at  10^  a  half -peck.     What  was  his  profit 
on  them  ? 


236 


SCHOOL    ARITHMETIC. 


Avoirdupois   Weight. 

339.    Avoirdupois  Weight  is  used  in  weighing  all  corn 
mon  articles. 


16  ounces  (oz.)  =  1  pound  (lb.). 
2000  pounds  =  1  ton  (T.). 

1.  How  many  ounces  in  4  lb.  ?    In  2J  lb.? 

2.  In  2  lb.  8  oz.  how  many  ounces? 

3.  What  part  of  a  pound  are  4  oz.?     10  oz.? 

4.  How  many  pounds  in  160  ounces?     In  336  oz.? 

5.  What  part  of  a  ton  is  500  lb.?     200  lb.? 

6.  A  barrel  of  flour  weighs   196   lb.      What   is   the 
weight  of  a  sack  of  flour  containing  J  of  a  barrel? 

7.  A  bushel  of  wheat  weighs  60  lb.    What  does  a  peck 
weigh? 

8.  From  a  firkin  of  butter  containing  42  lb.  a  grocer 
sold  13  lb.  10  oz.     How  much  was  left? 

\\)m          oz.  lb.  oz.  We  cannot  take  10  oz.  from  0 

40  Q      _      j_-j  -,  p  oz  ,  so  we  take  1  lb.  from  the 

1  A  1  Q  42  lb.  and  change  it  to  ounces. 

16  oz.  -  10  oz.  =  6  oz., 


286  28  6          and  41  lb-  —  13  lb-  =  28  lb- 

9.  A  butcher  sold  24  lb.  12  oz.  of  lard  from  a  can 
containing  40  lb.     How  much  was  left? 

10.  One    crock  of   butter    weighed  8  lb.  10  oz.,  and 
another  9  lb.  14  oz.     How  much  did  both  weigh? 

340.     1.     Find  the  cost  of  3i  lb.  of  cheese  at  12^  a 
pound. 

2.     What  will  3  lb.  8  oz.  of  butter  cost  at  20^  a  pound? 


COMPOUND    NUMBERS.  237 

3.  How  many  hundred  pounds  make  a  ton? 

4.  If  hay  is  worth  $20  a  ton,  what  is  100  Ib.  worth? 

5.  A  bushel  of  wheat  weighs  60  Ib.  How  many  bushels 
in  a  bag  weighing  120  Ib.? 

6.  A  bin  contains  6^  bu.  of  wheat.    What  is  the  weight 
of  the  wheat? 

7.  Three  boys  bought  2  Ib.  4  oz.  of  candy.    Each  paid 
15^.    How  many  ounces  should  each  one  receive? 

8.  If  a  man  eats  3  8-ounce  loaves  of  bread  in  one  day, 
how  many  pounds  will  he  eat  in  one  week? 

9.  A  bushel  of  oats  weighs  32  Ib.    Find  the  weight  of 
2  bu.  2  pk. 

10.  A  sack  of  oats  weighs  96  Ib.     What  is  it  worth 
at  30^  a  bushel? 

11.  At  $4  a  ton,  how  much  coal  can  be  bought  for  $25  ? 

12.  What  is  the  value,  at  $2  a  ton,  of  7000  Ib.  of  coal? 

Time  Measure. 
341.    Time  Measure  is  used  in  measuring  duration. 


60  seconds  (sec.)  =  1  minute  (min.). 
60  minutes  =  1  hour  (hr.). 

24  hours  —  1  day  (da.). 

7  days  =  1  week  (wk.).  • 

365  days  =  1  year  (jr.). 

12  months  (mo.)  =  1  year. 


238  SCHOOL    ARITHMETIC. 

1.  How  many  seconds    are    'there    in     5    "min.  ?      In 
10  min.? 

2.  How  many  hours  are  there  in  2  da.?     In  ^  da.? 

3.  How  many  days  are  there  in  2  weeks?     In  4  wk? 

4.  How  many  days  are  there  in  4  wk.  3  da.? 

5.  How  many  hours  in  240  min.?     In  180  min.? 

6.  100  years  make  1  century.     How  many  centuries 
in  1900  yr.? 

7.  In  1^  hr.  how  many  minutes? 

8.  What  part  of  a  day  is  6  hours?     16  hours? 

9.  How  many  days  in  this  month?    How  many  weeks? 

342.     1.     How  many  days  in  52  weeks?     Then  ,a  year 
is  how  much  longer  than  52  weeks? 

2.  How  long  is  it  from  Christmas  to  E"ew  Year's  Day? 

3.  How  many  months   is  it   from  one   Christmas   to 
another? 

4.  How  many  years  and  months  have  you  lived? 

5.  How  many  weeks  and  days  in  May? 

6.  How  many  times  does  the  clock  strike  12  every  day? 

7.  When  we  have  daylight  14  hours,  how  long  is  the 
night? 

8.  How  many  centuries  are  there  between  1300  and 
1900? 

9.  If  you  go  to  bed  at  9  o'clock  at  night  and  get  up  at 
6  in  the  morning,  how  long  are  you  in  bed? 

10.  Eight  hours  is  what  part  of  a  day?     16  hr.? 

11.  Cousin  Fred  came  to  our  house  on  Monday  arid 
stayed  2  weeks.     On  what  day  did  he  start  home? 

12.  If  a  train  runs  30  miles  an  hour,  how  far  does  it 
run  in  2  hours  and  a  half? 

13.  How  many  times  does  the  second  hand  of  a  watch 
go  around  while  the  minute  hand  goes  once  around? 


COMPOUND    NUMBERS.  239 

14.  While  the  hour  hand  goes  once  around,  the  minute 
hand  goes  around  -     -  times. 

15.  How  often  does  the  hour  hand  go  around  in  a  day? 
The  minute  hand? 

16.  How  many  minutes  in  f  of  an  hour? 

17.  Are  the  two  hands  of  a  clock  together  12  times  or 
13  times  in  12  hours? 

18.  If  a  boy  saves  10^  a  day,  how  much  will  he  save 
in  a  year? 

19.  If  a  man  earns  $30  a  month,  how  much  does  he 
earn  in  a  year? 

20.  A  girl  walked  J  mile  and  back  in  20  minutes. 
How  far  would  she  walk  in  an  hour  at  that  rate? 

21.  How  many  days  is  it  from  October  24  to  November 
3*     From  Dec.  25  to  Jan.  10? 

22.  If  a  man  gets  $2  for  working  8  hours,  how  much 
should  he  get  for  44  hours? 

23.  If  a  horse  can  trot  a  mile  in  3  minutes,  how  far 
can  he  trot  in  an  hour? 

24.  If  a  boy  walks  3  miles  an  hour,  how  far  does  he 
walk  in  4  hr.  40  min.? 

Long  Measure. 

343.    Long  Measure  is  used  in  measuring  lines   and 
distances. 


*   i   * l  i   *   i   *   i   *   i    *   i   *   i    *   i   * 
21     3|     4|     S|     6|     7|     8|     9| 


12    inches  (in.)  =  1  foot  (ft.). 

3    feet  =  1  yard  (yd.). 

54-  yards  ) 

16*  feet     }  =lrod(rd.). 

320    rods  =  1  mile  (mi.). 


24:0  SCHOOL    ARITHMETIC. 

How  many  feet  are  there  in  5  yards?  In  -J  of  a  yard? 
In  5J  yards? 

A  distance  of  5-|  yards  is  called  a  rod.  How  many  feet 
in  a  rod? 

A  barn  4  rods  long  is  how  many  yards  in  length?  How 
many  feet? 

How  many  rods  long  is  your  schoolroom?  Find  by 
measuring. 

Find  the  perimeter  of  a  field  32  rods  long  and  25  rods 
wide. 

Name  a  place  about  a  mile  from  your  home.  One  about 
2  miles.  One  about  half  a  mile. 

A  distance  of  320  rods  is  called  a  mile.  How  many  rods 
in  J  of  a  mile? 

In  J  of  a  mile  there  are rods ;  in  f  of  a  mile  there 

are rods. 

What  part  of  a  mile  is  160  rods?    80  rods? 

Complete: 

1.  1  rd.  2  yd.  = yd.  6.  1  mi.  40  rd.  =  -     -  rd. 

2.  3  ft.   2  in.  = in.  7.  6  yd.     2  ft.  =  -     -ft. 

3.  2  yd.  1  ft.  = ft.  8.  1  rd.     8  ft.  =  -     -ft. 

4.  1  yd.  4  in.  = in.  9.  1  mi.  80  rd.  =  mi. 

5.  2  rd.  2  ft.  = ft.  10.  1  yd.     1  ft.  1  in.=-      —in. 

344.  If  you  walk  20  rd.  a  minute,  how  long  will  it 
take  you  to  walk  a  mile? 

What  is  the  perimeter  of  a  field  80  rods  square? 

If  a  boy  walks  a  mile  to  school  in  20  minutes,  he  walks 
at  the  rate  of rods  a  minute  or miles  an  hour. 


COMPOUND    NUMBERS.  241 


What  is  the  length  of  this  line?  If  1  inch  represents  3 
feet,  what  does  the  line  represent?  Then  to  what  scale 
is  the  line  drawn? 

A  line  6  in.  long  is  drawn  to  the  scale  of  1  inch  to  3  feet. 
What  length  does  the  line  represent? 

Draw  a  line  5^  in.  long.  Let  each  inch  represent  3  feet. 
What  length  does  the  whole  line  represent? 

What  would  the  line  represent  if  the  scale  were  12  feet 
to  1  inch? 

^Making  each  inch  represent  10  feet,  draw  a  line  to 
represent  30  feet.  40  feet.  25  feet. 

A  field  is  48  rods  long  and  36  rods  wide.  Represent  it 
on  a  scale  of  12  rods  to  the  inch. 

A  township  in  some  states  is  a  mile  square.  Draw  a 
map  of  one  on  a  scale  of  1  inch  to  80  rods. 

345.     1.     A  room  18  ft.  long  is  how  many  yards  long? 

2.  A  fence  is  11  yards  or feet  or rods  long. 

3.  The  perimeter  of  a  rectangle  is  40  feet.     If  the 
length  is  12  feet,  what  is  the  width? 

4.  Ten  rods  is  how  much  greater  length  than  50  yards? 

5.  Find  the  distance  around  the  schoolhouse  in  feet. 
In  yards.     In  rods. 

6.  Frank  can  walk  3  miles  in  an  hour.     In  what  time 
can  he  walk  160  rods? 

7.  A  room  is  16J  ft.  square.     What  is  the  distance 
around  it? 

8.  What  part  of  a  yard  is  1  ft.  6  in.  ? 

9.  How  many  feet  and  inches  in  -J  of  a  rod? 
*i6 


24:2  SCHOOL    ARITHMETIC. 

10.  The  distance  to  the  moon  is  240,000  miles.  If  a 
bullet  traveled  1000  miles  an  hour,  it  would  reach  the 
moon  in  hours. 


B 

E 


D 

These  lines  represent  a  part  of  a  road.    They  are 
drawn  to  a  scale  of  1  inch  to  3  miles. 

11.  How  far  is  it  from  A  to  B?    From  B  to  C? 

12.  How  many  miles  is  it  from  D  to  E?    From 
C  to  D? 

13.  Find  the  distance  from  F  to  C.    From  F  to  A. 

14.  The  distance  from  E  to  D  is  what  part  of  the  dis- 
tance from  B  to  C? 

15.  A  man  wishes  to  drive  from  A  to  C.     When  he 
reaches  B,  what  part  of  the  distance  has  he  gone? 

16.  If  the  wheels  of  a  bicycle  turn  twice  around  in 
going  one  rod,  how  many  times  will  they  turn  in  going 
from  F  to  E? 

17.  A  room  is  18  ft.  long  and  15  ft.  wide.    The  carpet 
is  laid  lengthwise  and  is  a  yard  wide.     How  many  strips 
are  there  on  the  floor?    "What  is  the  length  of  each  strip? 
How  many  yards  in  all  the  strips? 

18.  If  the  carpet  is  a  yard  wide,  and  is  laid  lengthwise, 
how  many  yards  will  cover  the  floor  of  a  room  12  ft.  wide 
and  16  ft.  long? 


COMPOUND    NUMBERS. 


243 


Square  Measure. 
346.    Square  Measure  is  used  in  measuring  surfaces. 


144    square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.). 
9    square  feet  =  1  square  yard  (sq.yd.). 

30-J-  square  yards  =  1  square  rod    (sq.  rd.). 

160    square  rods  =  1  acre  (A.). 

We  have  learned  what  a  square  foot  is.  Draw  one,  and 
divide  it  into  square  inches. 

How  many  square  inches  in  one  row?     In  all  rows? 

Then  how  many  square  inches  make  1  square  foot? 

How  many  square  inches  in  2  sq.  ft.  ?  In  \  of  a  square 
foot? 

What  part  of  a  square  foot  is  72  sq.  in.?    36  sq.  in.? 

How  many  square  feet  are  there  in  288  sq.  in.? 

Draw  a  square  yard,  divide  it  into  square  feet,  and  find 
how  many  square  feet  make  1  square  yard. 

In  2  sq.  yd.  how  many  square  feet?    In  5  sq.  yd.? 

A  square  1  rod  long  and  1  rod  wide  is  called  a  square 
rod. 

How  many  square  rods  in  a  garden  5  rd.  long  and  3  rd. 
wide  ?  Make  a  map  of  the  garden,  letting  1  inch  represent 
a  rod. 


244 


SCHOOL    ARITHMETIC. 


Areas. 

347.  The  Area  of  a  surface  is 

the    number    of    square    units    of  All  B 

measure  it  contains. 

If  each  side  of  one  of  the  small 
squares  in  the  figure  is  one  inch 
long,  then  each  part  is  1  square 
inch  (square  unit  of  measure). 

The  area  of  the  strip  AB  is  4  X  1  sq.  in.,  or  4  sq.  in.7 
and  the  total  area  is  3  X  4  sq.  in.,  or  12  sq.  in. 

The  area  of  a  rectangle  is  expressed  by  the  product  of 
the  numbers  that  represent  its  length  and  width. 

348.  1.     How  many  square  feet  in  a  strip  of  carpet  a 
yard  wide  and  10  yards  long? 

2.  A  table  is  6  ft.  long  and  3  ft.  wide.     It  contains 
-  sq.  ft.,  or sq.  yd.   " 

3.  How  many  square  feet  of  oilcloth  will  cover  a  floor 
15  ft.  square?     How  many  square  yards? 

4.  Find  how  many  square  yards  would  be  needed  to 
cover  your  kitchen  at  home.     What  would  it  cost  at  30# 
a  square  yard? 

5.  A  lot  is  16  rd.  long  and  5  rd.  wide.     How  many 
square  rods  in  it?    What  part  of  an  acre? 

6.  What  part  of  an  acre  is  40  sq.  rd.?    120  sq.  rd.? 

7.  In  2  acres  how  many  square  rods?     In  5  A.?     In 
10  A.? 

8.  An  acre  and  40  sq.  rd.  =  -      -  A. 

9.  A  field  is  16  rd.  by  20  rd.     How  many  acres  in  it? 

10.  A  rug  is  9  feet  square.  How  many  square  feet  in  it? 

11.  The    area  of    a  rectangle  8  ft.  long  is  40  sq.  ft. 
What  is  the  width? 


COMPOUND    NUMBERS. 


245 


12.  The  perimeter  of  a  square  is  12  yards.     What  is 
the  area  in  square  feet? 

13.  A  rectangular  lot  is  50  ft.  by  75  ft.    The  house  on 
the  lot  is  25  ft.  by  50  ft.    How  many  square  feet  are  there 
in  the  yard? 

14.  How  many  square  inches  are  there  in  the  surface 
of  a  common  brick,  which  is  8  inches  long,  4  inches  wide, 
and  2  inches  thick? 

15.  A  farmer  wishes  to  make  a  grain  bin  8  ft.  long,  5 
ft.  wide,  and  4  ft.  deep.     Ho\v  many  square  feet  of  boards 
will  he  have  in  the  bottom?     In  one  end?     In  one  side? 


B 


D 


This  figure  is  drawn  to  a  scale  of  12  ft.  to  1  inch. 

349.    To  find  the  area  of  the  entire  figure  we  divide  it 
into  four  rectangles  and  find  the  area  of  each  separately. 

1.  What  is  the  length  of  A?     The  width?     The  area 
in  square  feet?     In  square  yards? 

2.  Find  the  area  of  B  in  square  feet.     In  square  yards. 
What  is  the  area  of  C?     The  area  of  D? 

Find  the  area  of  the  entire  figure  in  square  yards. 
How  does  the  area  of  A  compare  with  that  of  C? 
A  is  what  part  of  D?     D  is  what  part  of  B? 
What  part  of  the  entire  figure  is  B?  What  part  is  D? 
Copy  the  figure,  omitting  the  dotted  lines.     Make 


3. 
4. 
5. 
6. 

7. 
8. 


other  dotted  lines  dividing  the  figure  into  3   rectangles. 


Find  the  area  of  each  rectangle. 


246 


SCHOOL    ARITHMETIC. 


350.  Draw  a  rectangle  4  in.  long  and  3  in.  wide,  and 
divide  it  into  square  inches.  How  many  sq.  in.  have  you? 

Draw  another  rectangle  6  in.  long  and  2  in.  wide.  Is  its 
area  equal  to  that  of  the  first  rectangle?  Has  it  the  same 
dimensions  (length  and  width)? 

Draw  a  third  rectangle  12  in.  long  and  wide  enough 
to  have  the  same  area.  What  is  its  width? 

Draw  a  rectangle  6  in.  by  8  in.  Draw  another  twice  as 
long,  but  only  half  as  wide.  Are  their  areas  equal? 

Draw  another  twice  as  wide  as  the  first,  but  only  half 
as  long.  Compare  the  areas. 

What  may  be  the  dimensions  of  a  rectangle  containing 
24  sq.ft.?  36  sq.ft.?  64  sq.ft.? 

Complete : 

A  rectangle  6  in.  by  3  in.  equals  another  3  in.  by  -  —  in. 
A  rectangle  20  ft.  by  2  ft.  equals  another  10  ft.  by  -  -  ft. 
A  rectangle  5  in.  by  4  in .  equals  another  2-J  in.  by  -  -  in. 

A  rectangle  4  in.  by  7  in.  is  how  many  times  one  that  is 
2  in.  by  7  in.  ? 

A  rectangle  that  is  6  in.  by  5  in.  is  what  part  of  one  that 
is  9  in.  by  5  in.  ? 

HOWT  many  rectangles  each  2  in.  by  3  in.  are  equal  to  one 
that  is  6  in.  by  3  in.  ?  To  one  10  in.  by  3  in.  ? 


D 


B 


BASE 


351.   Point  out  the  base  of  the  shaded  triangle.     The 
altitude. 


COMPOUND    NUMBERS.  247 

What  part  of  the  rectangle  is  the  triangle? 

What  is  the  area  of  the  rectangle  ?    What,  then,  must  be 
the  area  of  the  triangle? 

The  area  of  the  rectangle  is  3  X  4  sq.  units. 

The  area  of  the  triangle  is  -J  of  3  X  4  sq.  units. 

The  area  of  a  triangle  is  expressed  by  one-half  of  the  pro- 
duct of  the  numbers  that  represent  its  base  and  altitude. 

1.     If  the  base  of  a  triangle  is  6  inches  and  the  altitude 
3  inches,  what  is  its  area? 

£  of  ( 3  X  6  )  sq.  in.  =  9  sq.  in. 

Find  the  area  of  the  following  triangles: 

2.  Altitude     8  inches,  base     6  inches. 

3.  Altitude  10  inches,  base     8  inches. 

4.  Altitude  12  inches,  base  12  inches. 

5.  Altitude     9  inches,  base  16  inches. 

6.  Altitude     5  inches,  base     3  inches. 

Cubic  Measure. 
352.    Cubic  Measure  is  used  in  measuring  solids. 

1728  cubic  inches  (cu.  in.)  =  1  cubic  foot  (cu.  ft.). 
27  cubic  feet  =  1  cubic  yard  feu.  yd.). 

Figure  1  represents  a  cubic 
inch.  Each  face  is  an  inch 
square.  Is  each  face  a  rectangle  ? 

Suppose  Fig.  1  is  drawn  to 
a  scale  of  1  foot  to  1  inch.  Then 
OD  represents  what  length? 

What  is  the  area  of  each 
face?  Does  the  figure  repre- 
sent a  cubic  foot  ?  FIG.  1 

A  solid  that  is  1  foot  long,  1  foot  wide,  and  1  foot  thick 
is  called  a  cubic  foot. 


248 


SCHOOL    ARITHMETIC. 


Find  a  block  of  wood,  a  stone,  or  a  box  that  is  about  as 
large  as  a  cubic  foot. 

Suppose  Fig.  1  is  drawn  to  a  scale  of  1  inch  to  3  feet, 
or  1  yard.  Then  OD  represents  what  length? 

What  is  the  area  of  each  face?  Does  the  figure  represent 
a  cubic  yard? 

A  solid  that  is  1  yard  long,  1  yard  wide,  and  1  yard 
thick  is  called  a  cubic  yard. 


353.  Figure  2  represents 
a  cubic  yard.  If  we  cut  it 
into  cubes  as  indicated,  what 
will  be  the  size  of  each  cube  ? 

Each  cube  is  a  cubic  foot. 
How  many  of  them  are 
there  in  one  layer?  In  the  3 
layers?  Then  how  many 
cubic  feet  in  a  cubic  yard? 


2. 


FIG.  3. 


354.  Fig.  3  represents  a 
cubic  foot.  If  we  cut  off  a 
piece  an  inch  thick  and  divide 
it  into  inch  cubes,  how  many 
of  them  shall  we  have? 

How  many  such  pieces  can 
be  cut  from  a  cubic  foot  ?  Then 
how  many  cubic  inches  in  a 
cubic  foot? 

A  cubic  yard  is  3  ft.  long,  3 
ft.  wide,  and  3  ft.  thick.  Find 
the  value  of  3  X  3  X  3.  Is 


the  product  the  number  of  cubic  feet  in  a  cubic  yard? 


COMPOUND    NUMBERS. 


249 


What  are  the  dimensions  of  a  cubic  foot?  Find  the 
value  of  12  X  12  X  12,  and  compare  it  with  the  number 
of  cubic  inches  in  a  cubic  foot. 

Find  how  many  cubic  inches  in  a  cube  that  measures  4 
inches  on  each  side.  Build  the  cube  with  blocks  (inch 
cubes). 

Volumes. 

355.  How  many  faces  has  a  cube?  Are  they  all  equal? 
Is  each  face  a  rectangle? 


FIG.  4 

Figure  4  represents  a  solid  6  inches  long,  4  inches  wide, 
and  3  inches  thick. 

How  many  faces  has  the  solid  ?    Is  each  face  a  rectangle  ? 

A  solid  bounded  by  6  rectangles  is  called  a  rectangular 
solid. 

In  Figure  4  each  little  cube  represents  1  cubic  inch. 
Find  how  many  cubic  inches  there  are. 

There  are  three  layers,  each  containing  4  rows  of  the  little  cubes, 
as  ABCD.  Each  row  contains  6  little  cubes,  or  cubic  inches,  hence 
the  4  rows  contain  24  cubic  inches. 

Since  there  are  24  cu.  in.  in  each  layer,  in  the  3  layers  there  are 
3  X  24  cu.  in.,  or  72  cu.  in.,  which  is  the  volume. 

Find  the  value  of  6  X  4  X  3.  Does  the  product  equal 
the  number  of  cubic  inches  in  Fig.  4?  (6  X  3  X  4)  X 
1  cu.  in.  =  -  -  cu.  in. 

The  volume  of  a  rectangular  solid  is  expressed  by  the 


250  SCHOOL    ARITHMETIC. 

product  of  the  numbers  that  represent  its  length,  breadth, 
and  thickness. 

The  number  of  cubic  units  (cu.  in.,  cu.  ft.,  cu.  yd.,  etc.)  in  a  solid 
is  called  its  volume. 

1.  How  many  cubic  inches  in  a  brick  8  in.  long,  4  in. 
wide,  and  2  in.  thick? 

2.  How  many  cubic  feet  in  a  wall  16  ft.  long,  4  ft. 
high,  and  2  ft.  thick? 

3.  A  hole  is  3  ft.  long,  2  ft.  wide,  and  6  ft.  deep.  How 
many  cubic  feet  of  earth  have  been  removed? 

4.  A  cistern  is  6  ft.  square  and  9  ft.  deep.    How  many 
cubic  feet  of  water  will  it  hold?    How  many  cubic  yards? 

5.  How  many  cubic  feet  in  a  cord? 

A  pile  of  wood  8  ft.  long,  4  ft.  wide,  and  4  ft.  high  is  called  a  cord. 

6.  How  many  cords  are  there  in  a  pile  of  wood  16  ft. 
long,  4  ft.  wide,  and  4  ft.  high? 

7.  A  cubic  foot  of  water  weighs  1000  oz.    What  is  the 
weight  of  a  cubic  yard  of  water? 

8.  Find  the  dimensions  of  a  box  that  will  hold  24  cu. 
in.  of  water. 

9.  What  are  the  width  and  depth  of  a  cistern  6  ft.  long 
that  will  hold  144  cu.  ft.  of  water? 

10.  An  ice  box  holds  20  cu.  ft.  of  ice.      It  is  4  ft.  long 
and  2  ft.  deep.     How  wide  is  it  ? 


DECIMAL    FRACTIONS. 


251 


Decimal  Fractions. 
A  B 


356.  What  part  of  A  is  dark?    Into  how  many  parts  is 
each  strip  divided  in  B? 

What  part  of  each  strip  is  the  shaded  square  ?  What  part 
of  the  large  square? 

Then  -^  of  one-tenth  of  B  is  one  -     -  of  B. 

When  anything  is  divided  into  ten  equal  parts,  what  is 
each  part  called? 

When  each  of  these  ten  parts  is  divided  into  ten  parts, 
how  many  parts  are  there? 

When  each  of  these  hundred  parts  is  divided  into  ten 
parts,  how  many  parts  are  there? 

When  anything  is  divided  into  tenths,  hundredths,  thousandths,  etc., 
the  parts  are  called  decimal  parts  ;  that  is,  tenth-parts. 

357.  You    have    already  learned    that  10  hundredths 
make  1  tenth,  and  that  10  tenths  make  1  one,  just  as  10 
ones  make  1  ten,  10  tens  1  hundred,  and  so  on.    You  have 
also  learned  that  tenths  and  hundredths  may  be  written 
with  the  decimal  point  and  without  denominators.     Frac- 
tions so  written  are  called  Decimals  or  Decimal  Fractions. 

358.  Tenths  must  stand  next  to  ones,  because  10  of 
them  make  1  one;  hundredths  next  to  tenths,  because  10 


252 


SCHOOL    ARITHMETIC. 


of  them  make  1  tenth.    Kext  to  hundredths  we  must  write 
thousandths,  because  10  of  them  make  1  hundredth,  etc. 

359.  In  decimals,  as  in  integers  (whole  numbers),  the 
position  of  the  figures  indicates  their  value.     Thus,  in  3.15 
we  know  that  the  1  is  one-tenth,  because  tenths  are  written 
only  in  the  first  place  to  the  right  of  ones;  and  that  the  5 
is  five  hundredths,  because  it  is  in  the  second  place. 

360.  One-tenth  of  a  cent  is  called  a  mill;  then  how 
many  mills  make  1  cent  ? 

How  many  mills  in  10  cents?  In  100  cents,  or  $1? 
Then  1  mill  is  what  part  of  a  dollar? 

What  part  of  a  cent  are  5  mills,  or  5  thousandths  of  a 
dollar? 

In  $.125,  how  many  dimes,  cents,  and  mills?  Which 
figure  is  in  tenths'  place  ?  In  hundredths'  ?  In  thousandths'  ? 

How  many  mills  make  1  cent,  or  1  hundredth  of  a  dollar  ? 

How  many  mills  in  1  dime?  In  2  cents?  Then  may 
$.125  be  read  as  125  mills,  or  as  125  thousandths  of  a 
dollar? 


1  ^  S  *  £ 
3  O  g  s  2 
o>  ~  LR  o>  fl 


a)   .2    w 

2±   gc5 


H  PH  H  H 
12345.    6789 


Integers.        Decimals. 


361,     Examine  this  table.     Ten  of  any  order  make  one 
of  the  next  higher  order.    With  reference  to  ones,  wliciv 


DECIMAL    FRACTIONS.  253 

are  tens  and  tenths  written?     Hundreds  and  hundredths? 
In  what  place  is  the  8?    What  does  it  express? 

In  the  decimal  .125,  there  are  1  tenth,  2  hundredths,  and 
5  thousandths,  or  125  thousandths.  When  there  are  no 
tenths  or  hundredths,  we  write  thousandths  in  the  third 
place,  and  put  ciphers  in  the  first  two  places. 

Thus,  5  thousandths  is  written  .005. 

What  decimal  place  is  occupied  by  tenths?  By  thou- 
sandths? By  hundredths? 

What  occupies  the  second  decimal  place?  The  fourth? 
The  third? 

Extend  tho  table,  and  tell  what  occupies  the  fifth  place. 
The  sixth  place. 

362.  In  reading  integers  we  omit  the  name,  which  is 
ones,  the  name  of  the  lowest  integral  order.  Decimals  are 
read  just  as  integers  are,  except  that  the  name  of  the  lowest 
decimal  order  is  given. 

In  reading  an  integer  and  decimal,  use  the  word  and 
between  the  integral  and  decimal  parts  of  the  number,  but 
nowhere  else. 

325.46       is  read  325   and     46  hundredths. 

73.05       is  read     73  and       5  hundredths. 

.08       is  read       8  hundredths. 
517.325     is  read  517  and  325  thousandths. 

82.073     is  read     82  and     73  thousandths. 
716.0034  is  read  716  and     34  ten-thousandths. 


254:  SCHOOL    ARITHMETIC. 

363.  Eead  the  following: 

x.  .7  10.  .225  19.  278.35 

2.  .15  11.  .600  20.       51.07 

3.  .38  12.  .012  21.       39.50 

4.  .03  13.  .708  22.  624.054 

5.  .44  14.  .1325  23.  516.0027 

6.  .044  15.  .4016  24.       88.0008 

7.  .444  16.  .7203  25.  200.0200 

8.  .707  17.  .0518  26.  765.4004 

9.  .005  18.  .0024  27.  394.3275 

364.  Write  7  thousandths  as  a  decimal. 

Thousandths  occupy  the  third  place,  hence  we  write  the  7  and  put 
ciphers  in  the  first  two  places,  thus  :   .007. 

Express  25  thousandths  as  a  decimal. 

25  thousandths  =  2  hundredths  and  5  thousandths.     There  are  no 
tenths,  hence  we  put  a  cipher  in  the  first  place,  thus  :  .025. 

Write  as  decimal  fractions : 

5  tenths  216  thousandths  75  thousandths 

7  hundredths  103  thousandths  40  thousandths 
42  hundredths  68  hundredths  90  hundredths 

8  thousandths  50  hundredths  6  thousandths 
36  thousandths  9  thousandths  82  thousandths 

5  and  37  hundredths  46  and  7  thousandths 

24  and     5  hundredths  75  and  14  thousandths 

17  and     9  tenths  8  and  125  thousandths 

32  and     8  hundredths  92  and  8  thousandths 

40  and  40  hundredths  72   and  72  thousandths 


DECIMAL    FRACTIONS.  255 

Addition  and  Subtraction. 

365.     1.    Add  .7,  .42,  .05,  2.7,  and  15.48. 
.7 

Are  the  tenths  all  written  in  the  same  column  ?  Where 
•  05         are  the  hundredths   written?     How  are  the  decimal 
2 .  T  points  arranged  ? 

15.48  Are  decimals  added  just  as  integers  are  added  ? 


19.35 

2.     Subtract  .17  from  .56,  and  .24  from  .8. 

.56  .8  Are  tenths  written  in  one  column?    Can  you 

.17  .24        ta>ke  4  hundredths  from  no  hundredths?     What 

must  you  do  ?     Do  we  subtract  as  in  whole  'num- 


39          .56       bers? 


Add: 

3 

4 

5 

6 

42.3 

13.256 

7.0296 

.032 

16.07 

6.09 

5.724 

.85 

5.45 

54.307 

38.602 

.027 

.08 

8.9 

3.08 

.645 

24.06 

36.005 

6.7043 

.930 

Subtract  : 

7 

8 

9 

10 

11 

37.42 

51.63 

7.15 

.672 

.0072 

12.51 

28.35 

6.47 

.348 

.0036 

12 

13 

14 

15 

16 

2.57 

5.02 

16.3 

.207 

.87 

.39 

2.75 

2.14 

.0525 

.254 

256  SCHOOL    ARITHMETIC. 

Find  the  value  of: 

17.  72.5 +  .324  + 5.07  23.  6.08  +  .027  —  4.44 

18.  61.3  +  2.79  +  .008  24.  8.72  +  .803  —  .75 

19.  26.7 +.41.3  +  .802  25.  3.60  +  34.2  —  .016 

20.  5.34  + .534  + 53.4  26.  .542  +  7.61  —  3.25 

21.  .016  +  0.16  +  .024  27.  9.27 —  3.45  —  .005 

22.  7.03 +  .300 +5.04  28.  .172  +  61.5  —  2.64 

Multiplication  and  Division. 

366.   How  many  tenths  are  5X6  tenths?     30  tenths 
are  equal  to  how  many  ones?    3.0   =   30  tenths. 

How  many  tenths  are  8X5  tenths  ?    40  tenths  =  - 
ones. 

5  x  .6  =  30  tenths,  or  3.     8X5  tenths  =  40  tenths,  or  4. 

In  25  tenths,  how  many  ones  and  tenths? 

1.    Multiply  4.2  by  6. 

4.  2  6X2  tenths  =  12  tenths,  or  1.2.     Where  do  we  write 

*  «  the  2  ?    What  is  done  with  the  1  ?    Do  we  multiply  as 

in  whole  numbers  ?    How  many  decimal  places  in  the 


25.2  factors  ?    How  many  in  the  product  ? 

There  must  be  as  many  decimal  places  in  the  product  as 
there  are  in  both  factors. 

Find  the  products: 

2.  5  X  3.7  7.     2  X  .24  12.  4  X  1.36 

3.  7  X  2.3  8.     5  X  .13  13.  7  X  3.35 

4.  4  X  5.6  9.     4  X  .23  14.  3  X  8.72 

5.  6X1.7  10.     7.X  .14  15.  .12  X  .48 

6.  8  X  4.2  11.     8  X  .06  16.  2.4  X  1.2 


DECIMAL    FRACTIONS.  257 

17.     Multiply  .14  by  .7. 

7  X  14  =  98,   only  two  places.    What  must  we  do 
•  7  to  make  three  places  ?    How  do  we  know  there  should 

be  three  decimal  places? 


Find  the  products: 

18.  .5  X  .5                23.  12.5  X  .5  28.  .48  X  .4 

19.  .8  X  .4                24.  16.3  X  .2  29.  .25  X  .5 

20.  .6  X  .6                25.  24.6  X  .3   .  30.  .32  X  .3 

21.  .9  X  .3                26.  33.2  X  .4  31.  .17  X  .5- 

22.  .7X.8                27.  53,2  X  .5  32.  .55  X  .3 
33.     Multiply  142  by  .06. 

on  How  many  decimal  places  in  the  factors?    Then  how 

many  must  we  point  off  in  the  product? 

8.52 

.Multiply: 

34.  125  by  .03  39.     376  by  .05 

35.  234  by  .06  40.     428  by  .03 

36.  145  by  .05  41.     706  by  .06 

37.  421  by  .04  42.     250  by  .07 

38.  845  by  .06  43.     625  by  .05 
367.   'What  is  i  of  8  tenths?    -J  of  .8  = 

What  is  i  of  9  tenths?    J  of  .9  = 
What  is  i  of  24  hundredths?    i  of  .24  = 
What  is  ^  of  18  tenths?     i  of  1.8  = 
What  is  i  of  36  tenths?     J  of  3.6  = 
Copy  and  find: 

1.  i  of  .6  4.  4  of  2.4  7.  4  of  36  tenths,  or  3.6 
2.-  ]of  .8  5.  -J  of  3.9  8.  i  of  52  tenths,  or  5.2 
3.  -J  of  .6  6.  i  of  8.4  9.  -J  of  42  tenths,  or  4.2 


258  SCHOOL    ARITHMETIC. 

Copy*  and  complete: 


10. 

11. 

12. 
13. 
14. 
15. 

3)126 

3)  12.6 

3)  13.5 

3)  13.8 

4)168 

4)  16.8 

4)  17.2 

4)  17.6 

6)  126 

6)  12.6 

6)  13.2 

6)  14.4 

8)  168 

8)  16.8 

8)  17.6 

8)  18.4 

7)217 

7)  21.7 

7)  22.4 

7)  23.1 

4)568 

4)  56.8 

4)  57.2 

4)  59.6 

16.  Divide  75  by  4. 

4)  75. 00  7  tens  -=-4=1  ten,  and  3  tens  remaining. 

35  ones  -^4  =  8  ones,  and  3  ones  remaining. 
L8.75  3  oneg  and  Q  tenths  =  30  tenths.     30  tenths  -r-  4  = 

7  tenths,  and  2  tenths  remaining.     2  tenths  and  0 
hundredths  =  20  hundredths.     20  hundredths  -j-  4  =  5  hundredths. 

Find  the  quotients: 

17.  49  -r-  4             21.     71  -T-  5  25.  121 -r- 8 

18.  67  -f-  4             22.     79-^4  26.  130^-8 

19.  53-^-4              23.     35  -f-  2  27.  146  -f-  4 

20.  66 -f- 5              24.     87-^-2  28,  255-^-6 
368.   How  many  tenths  in  1?    In  2?  In  4?    In  2J  < 
How  many  hundredths  in  1?    In  J?  In  i? 

Write  as  decimals:  £,  i,  },  J,  f,  f ,  TV,  iV 

How  many  thousandths  in  1?     In  J?  In  i? 

Write  as  decimals:  -J,  f,  f,  5,  -j^V 

Change  to  common  fractions:    .5,  .25,  .75,  .2,  .075. 

The  following  exercises  will  show  you  that — 

(a)  Moving  the  decimal  point  one  place  to  (lie  right 
multiplies  a  number  by  10. 

(b)  Moving    the    decimal  point  one  place  to  the  left 
divides  a  number  by  10. 


DECIMAL  FRACTIONS.                                          259 

1.  10X2.5  =  25.  6.     25.0  -4- 10  =  2.5 

2.  10X1.25  =  12.5  7.     12.5-^10  =  1.25 

3.  10  X. 25  =  2.5  8.     2.5  -=-  10  =  .25 

4.  10  X. 5  =  5.0  9.     5.0 -4- 10  =  .5 

5.  10  X  .05  =  .5  10.     .5  —  10  =  .05 

Find  the  products  and  quotients  by  moving  the  decimal 


point  : 

11. 

10 

X 

2.7 

17. 

27- 

_i_ 

10 

23. 

10 

X 

4.265 

12. 

10 

X 

2.45 

18. 

24. 

5- 

•4-10 

24. 

10 

X 

30.74 

13. 

10 

X 

.36 

19. 

3.6 

-4-10 

25. 

10 

X 

261.7 

14. 

10 

X 

.8 

20. 

8.  - 

10 

26. 

37 

5  X  10 

15. 

10 

X 

.07 

21. 

.7  - 

•5— 

10 

27. 

62 

5.4 

X  10 

16. 

10 

X 

1.03 

22. 

10.3 

•4-10 

28. 

71 

.68 

X  10 

Complete  the  following  and  show  that — 

(c)  MDriiif/   the   decimal  point  two  places  to  the  riyht 
m  ultqdi-es  a  number  by  100. 

(d)  Moving    the    decimal  point  two  places  to  the  left 
divides  a  number  by  100. 

29.  100  X  25.0  =  39.  2500  -f- 100  = 

30.  100  X  1.25  =  40.  1 25  -4- 100  = 

31.  100 -X  12.5=  41.  1250-^-100  = 

32.  100  X. 125=  42.  12.5-4-100  = 

33.  100  X  .042  =  43.  4.2  -4- 100  = 

34.  100  X. 005=  44.  .5-4-100  = 

35.  100  X  3.07  =  45.  307  -4- 100  = 

36.  100  X. 5=  46.  50-^-100  = 

37.  100  X  .25  =  47.  25  -4-  100  - 

38.  100  X  .05=  48.     5-1-100  = 


260  SCHOOL    ARITHMETIC. 

369.  1.     Divide  .098  by  .7. 

.098  -i-  .7  =   .14  Is  -098  tne  product  of  .7  (the  divisor)  and 

.14   (the  quotient)  ?      Does  it  contain   as 
many  decimal  places  as  both  the  factors. 

The  dividend  contains  3  decimal  places,  the  divisor  1.     How  many 
must  the  quotient  contain  ? 

There  must  be  as  many  decimal  places  in  the  quotient 
<as  the  number  of  such  places  in  the  dividend  exceeds  the 
number  in  the  divisor. 

Find  the  products:  Find  the  quotients: 

1.  .6  X  .7  8.  .42  -*-  .6 

2.  .3  X  .15  9.  .45  +  .3 

3.  .5  X  4.3  10.  2.15  -5-  .5 

4.  3.6.X  .$  11.  3.24  -f-  .9 

5.  .7  X  .05  12.  .035  ~  .7 

6.  .9  X  -017  13.  .0153  -*-  .0 

7.  310  X  .05  14.  15.50  ~  .05 

370.  Another  name  for  hundredths  is  per  cent.     Instead 
of  saying  5  hundredths  of  $250,  we  may  say  5  per  cent  of 
$250. 

To  find  1  hundredth  of  a  number  we  divide  it  by  100. 
Hence,  to  find  1  per  cent  of  a  number  we  divide  the  num- 
ber by  100. 

What  is  the  easiest  way  to  divide  by  100? 

1.  Find  1  per  cent  of  $125. 

$125 -f- 100  =  $1.25. 

2.  Find  1  per  cent    of  $275.     Of  $325.     Of  $152.50. 

3.  What  is  1  per  cent  of  $200?     What  is  2  per  cent 
of  $200? 

4.  Tind  2  per  cent  of  $300.    Of  $500.    Of  $250. 


PERCENTAGE. 


261 


5.  What  is  3  per  cent  of  $217.50?     Of  $187.50? 

6.  When  you  know  what  1  per  cent  of  a  number  is, 
how  do  you  find  4  per  cent  of  the  number? 

7.  Find  4  per  cent  of  $732.50.     Of  $364.25. 

8.  What  is  6  per  cent  of  $75?     Of  $87.25? 

9.  Find  5  per  cent  of  200.     Of  800.     Of  24.5. 

10.  What  per  cent  of  a  number  equals  100  hundredths 
of  the  number? 

11.  Multiply  $125  by  .05,  and  compare  the  product 
with  5  per  cent  of  $125. 

12.  Find  6  per  cent  of  $240;  multiply  $240  by  .06. 
Are  the  results  equal? 

13.  Compare  .04  X  $325  with  4  per  cent  of  $325.  Are 
they  equal? 

14.  In  how  many  ways  can  you  find  a  per  cent  of  a 
number? 

15.  If  you  borrow  money,  do  you  have  to  pay  anything 
for  its  use? 

16.  Find  out  at  home  all  you  can  about  what  is  paid  for 
the  use  of  money. 

Percentage. 


371.  This  square  is  di- 
vided into  —  —  equal  parts. 
Each  part  is  1  -  -  of  the 
square. 

What  part  of  the  square 
is  A  +  B? 

How  many  hundredths  of 
the  square  in  each  horizon- 
tal strip?  Each  strip  is  what 
part  of  the  square? 


262  SCHOOL    ARITHMETIC. 

Instead  of  hundredths  we  may  use  the  term  per  cent, 
because  per  cent  means  hundredths. 

Then  what  per  cent  of  the  square  is  A  ?    A  +  B  ? 

How  many  per  cent  are  there  in  the  square?  In  any- 
thing? 

One  hundred  per  cent  of  a  number  is  the  number  itself. 

What  per  cent  of  the  square  is  above  the  line  KIM 
What  part  of  anything  is  50  per  cent  of  it? 

What  part  of  the  square  is  shaded  ?  What  per  cent  of  it 
is  shaded? 

How  many  small  squares  in  10  per  cent  of  the  large 
square?  In  20  per  cent? 

The  sign  %  stands  for  the  term  per  cent,  and  means 
either  per  cent  or  hundredths.  Thus,  5%  of  the  square 
means  5  per  cent,  or  5  hundredths  of  it. 

What  per  cent  of  the  square  isA  +  B  +  C  +  D  +  E? 

What  part  of  the  square  is  10$  of  it?  20$?  4<K/< 
50$?  60$?  6$? 

Cover  25%  of  the  square.    What  %  is  not  covered? 

372.  What  %  of  $100  is  $5?     $10?     $25? 

Draw  a  rectangle  and  divide  so  as  to  show  50%  of  it. 
25%.  12^%. 

Divide  a  square  so  as  to  show  that  50%  =  2?  and  that 
25%  =J. 

'  Draw  a  line  an  inch  long,  and  another  line  50%  as  long. 
;  This   line   is   an   inch   long.      • —  — .      Draw 

another  line  100%  as  long. 

How  many  times  a  number  is  200%  of  it?    300%? 

3^  of  a  number  is  what  %  of  it  ? 

How  do  you  find  1  hundredth,  or  1%,  of  a 


PERCENTAGE.  263 

What  is  the  effect  of  moving  the  decimal  point  two  places 
to  the  left? 

When  you  have  found  1%  of  a  number,  how  do  you  find 
3%  of  it?  5%? 

Find  1%  of  200.    Of  500.    Of  250.    Of  12.5. 

Find  5%  of  200.    Of  125.    Of  315.    Of  41.2. 

State  the  simplest  way  of  finding  10%,  or  y1^-,  of  a  num- 
ber. What  is  the  effect  of  moving  the  decimal  point  one 
place  to  the  left? 

Find  10%  of  50.    Of  12.5.     Of  345.     Of  624. 

What  is  the  ratio  of  200%  to  100%?  100%  to  50%? 
25%  to  100%? 

What  .is  100%  of  5^?    Of  $10?     Of  25  gal.? 

373.  1.  Find  2^%  of  $400. 

\%  of  $400  =  ^4.00. 
2\%  of  $400  =  2|  X  $4.00,  or  $10. 

Find: 

2.  1J  %  of  $1200.  6.     334  %  of  900  ft. 

3.  12^%  Of  $000.  7.       2i%  of  $1500. 

4.  16|  %  of  120  bu.  8.         4  %  of  $1000. 

5.  17    %  of  $320.  9.         f  %  of  $2000. 

374.  Be  sure  you  understand  the  following: 
100   %  of  a  number  =  all  of  it. 

200   %  of  a  number  =  twice  the  number. 

25.  %  of  a  number— |  of  it. 

12i%  of  a  number  =  |  of  it, 

37^-%  of  a  number  =  f  of  it. 

33i%  of  a  number  =  4  of  it. 

1.  Find  200%  of  $5.     Of  3  ft.      Of  £  gal. 

2.  What  is  25%  of  24  in.?    Of  16  ft.?    Of 


264  SCHOOL    ARITHMETIC. 

3.  Find  50%  of  $20.  Of  $.40.    Of  a  dime.    Of  a  gallon. 

4.  Find  12^%  of  40^.     Of  8  yd.     Of  4  bu.     Of  72  ft. 

5.  What  is  33-J%  of  a  yard?    Of  12  qt?     Of  $300? 

6.  A  man  who  had  $10  spent  50%  of  it.     How  much 
had  he  left? 

7.  Mr.  Lee  has  40  acres  of  land.     If  he  plants  25% 
of  it  in  corn,  how  many  acres  does  he  plant? 

8.  How  many  days  in  33^%  of  the  month  of  June? 

9.  If  $6  is  50%  of  my  cash,  how  much  have  I? 

10.  0  is  i  of  what  number?    6  is  20%  of  what  number? 

11.  A  farmer  had  80  chickens,  but  a  hawk  caught  25% 
of  them.    How  many  did  the  farmer  have  left? 

12.  What  is  the  difference  in  hours  between   1G|% 
and  12^%  of  one  aay$ 

13.  Eva's  age  is  75%  of  the  age  of  Ethel,  who  is  16 
years  old.     How  old  is  Eva? 

14.  Pencils  bought  at  48^  a  dozen  were  sold  at  a  gain 
of  25%.    Find  the  selling  price  of  each  pencil. 

15.  A  girl  spelled  correctly  99%  of  200  words.     How 
many  did  she  miss? 

16.  Some  boys  bought  a  pie,  and  each  ate  25%  of  it. 
If  the  whole  pie  was  consumed,  how  many  boys  were  there  ? 

17.  What  is  the  distance  between  two  towns  if  5  miles 
is  33^%  of  the  distance? 

18.  I  had  $20,  but  spent  $10  of  it  for  a  dress.     What 
per  cent  of  rny  money  did  I  spend? 

19.  A  farmer  who  had  8  cows  sold  2  of  them.     \Ylml, 
per  cent  of  them  did  he  sell? 

20.  I  bought  a  stove  for  $12  and  sold  it  so  as  to  gnin 
$3.    What  per  cent  of  the  cost  did  I  gain? 

Gain  or  loss  is  always  some  per  cent  of  the  cost. 


PEKCENTAGE.  205 

21.  A  boy  bought  a  watch  for  $12  and  sold  it  for  $9. 
How  much  did  he  lose?    What  per  cent  of  the  cost? 

22.  Robert  paid  $15  for  an  overcoat  and  sold  it  for 
$20.    What  per  cent  did  he  gain? 

23.  If  I  pay.  $2  for  an  article  and  sell  it  for  $1,  what 
per  cent  do  I  lose  ? 

24.  If  a  sheep  is  bought  for  $4  and  sold  at  a  gain  of 
_!r>%,  for  how  much  is  it  sold? 

25.  A  man  paid  50^  for  a  knife  and  sold  it  at  a  loss  of 
10%.      What  did  he  get  for  it? 

26.  If  a  grocer  buys  sugar  at  4#  a  pound  and  sells  it  at 
r>^  a  pound,  what  per  cent  does  he  gain? 

27.  At  what  price  must  coffee  which  cost  15^  a  pound 
be  sold  to  make  a  profit  of  20%? 

28.  How  much  must  be  paid  for  a  book  marked  $2,  if 
25%  is  taken  off  the  marked  price? 

29.  If  $12  is  37  2%  of  my  money,  how  much  have  I? 

30.  An    organ    which    was    marked  $70  I  bought  for 
10%  less.     Tell  me  what  I  paid  for  it. 

31.  Of  a  regiment  of  1000  soldiers  5%   were  made 
prisoners.     How  many  escaped? 

32.  How  much  must  be  paid  for  a  bicycle,  if  the  marked 
price  is  $75,  and  the  discount,  or  the  sum  taken  off,  is  40%  ? 

33.  What  per  cent  of  the  day  has  passed  at  6  o'clock 
A.  M.? 

34.  Oranges  were  bought  at  the  rate  of  2  for  5#,  and 
sold  at  3^  apiece.    What  per  cent  was  gained? 

35.  A  man  who  earned  $60  a  month  had  his  salary 
increased  25%.     He  then  earned  $ —    -  a  month. 

36.  If  you  get  6  cents  interest  for  every  100  cents  you 
loan  for  a  year,  what  per  cent  are  you  getting? 


266  SCHOOL    ARITHMETIC. 


Interest. 

375.  If  a  man  borrows  a  horse,  he  does  not  pay  for  its 
use;  if  he  hires  the  horse,  he  must  pay  the  owner  whatever 
is  agreed  upon. 

When  a  man  borrows  money,  he  is  usually  required  to 
pay  something  for  its  use.  Money  paid  for  the  use  of 
money  is  called  Interest. 

1.  If  you  borrow  $100  from  me  and  agree  to  pay  me 
6%  a  year  for  its  use,  at  the  end  of  the  year  you  must 
give  me  back  the  $100  and  pay  me  the  interest,  which  is 

6%  of  $100,  or  $-    — . 

2.  If  you  borrow  $100  at  4%  a  year,  how  much  interest 
will  you  owe  at  the  end  of  one  year? 

3.  What  is  the  interest  of  $100  for  1  year  at  5%? 

4.  At  6%,  what  i.s  the  interest  of  $200  for  1  year? 
Of  $500?    Of  $300? 

5.  At  4%,  what  is  the  interest  of  $300  for  1  year? 
For  2  years? 

6.  At  3%,  what  is  the  interest  of  $400  for  1  year? 
For  2  years? 

7.  Find  the  interest  of  $300  for  1  year  at  6%.     For 
2  years. 

8.  At  6%,  what  is  the  interest  of  $200  for  6  months  ^ 

9.  At  5%,  what  is  the  interest  of  $600  for  4  months 
(iyr.)? 

10.  At  6%,  what  is  the  interest  of  $200  for  1  year 
and  6  months  (1J  yr.)? 


INTEREST.  267 

376.    Find  the  interest  of  $200  for— 

1.  2  yr.  @  6%  7.  2  yr.  @  8% 

2.  5  yr.  @  6%  8,  6  yr.  @  8% 

3.  6  mo.  @  Q%  9.  3  yr.  @  3% 

4.  3  mo.  @  6%  10.  4  mo.  @  3% 

5.  2  mo.  @  6%  11.  6  mo.  @  4% 

6.  9  mo.  @  6%  12.  9  mo.  @  4% 

13.     Find  the  interest  of  $150  at  4%  for  2  yr.  3  mo. 

$1.50  =  interest  for  1  yr.  at  \%. 
4 

$6.00  =  interest  for  1  yr.  at  4%. 
2 


$12.00  =  interest  for  2  yr.  at  4$. 

1.50  =  interest  for  3  mo.  (\  yr. )  at  4%. 

$13.50  =  interest  for  2  yr.  3  mo.  at  4%. 

Find  the  interest  of  $150  for — 

14.  3  yr.  4  mo.  @  4%            16.     2  yr.  9  mo.   @  4-.% 

15.  4  yr.   6  mo.   @  4%            17.     5  yr.  2  mo.   @  4% 

Find  the  interest  of  $240  for— 

18.  1  yr.  3  mo.  @  5%     25.  5  yr.  2  mo.  @  2% 

19.  3  yr.  0  mo.  @  6%     26.  7  yr.  4  mo.  @  8% 

20.  2  yr.  4  mo.  @  4%     27.  1  yr.  1  mo.  @  4% 

21.  4  yr.  8  mo.  @  4%     28.  3  yr.  9  mo.  @  6% 

22.  1  yr.  9  mo.  @  6%     29.  4  yr.  2  mo.  @  5% 

23.  6  yr.  6  mo.  @  3%     30.  10  yr.  4  mo.  @  7% 

24.  8  yr.  4  mo.  @  5%     31.  16  yr.  8  mo.  @  6% 


208  SCHOOL    ARITHMETIC. 

GENERAL    REVIEW. 
Oral  Work. 

377,     1.     A  man  bought  a  book  for  56^  and  gave  a 
silver  dollar  in  payment.     Count  up  the  change. 

2.  How  many  handkerchiefs  at  25^  each  can  be  bought 
for  $3? 

3.  Find  the  perimeter  of  a  rectangle  8  ft.  long  and  50% 
as  wide. 

4.  If  C  men  can  build  a  stable  in  8  days,  how  long 
would  it  take  one  man? 

5.  If  one  man  can  build  a  wall  in  32  days,  how  long 
would  it  take  4  men? 

6.  If  5  cows  are  worth  25  sheep,  8  cows  are  worth'  — 
sheep. 

7.  How  many  pounds  of  butter  at  12#  a  pound  must  be 
given  for  3  Ib.  of  coffee  at  16^  a  pound? 

8.  At  the  rate  of  3  for  5#,  how  many  oranges  can  be 
bought  f or  $1? 

9.  James  bought  3  bushels  of  pears  at  $2  a  bushel. 
Henry  bought    twice  as  many  at  the  same    price.     How 
much  did  both  pay? 

10.  Lemons  were  bought  at  the  rate  of  2  for  5#,  and 
sold  at  3^  apiece.     Find  the  gain  on  a  dozen. 

11.  A  grocer  paid  75^  a  bushel  for  potatoes  and  sold 
them  at  25^  a  peck.    How  much  did  he  gain  on  10  bushels? 

12.  What  is  the  ratio  of  a  gallon  to  a  pint? 

13.  A  farmer  had  40  sheep.     Dogs  killed  one  out  of 
every  8.    How  many  were  not  killed? 

14.  If  10  men  weigh  a  ton,  what  is  the  average  weight 
of  each  man? 


GENERAL    REVIEW.  2<>9 

15.  How  many  square  inches  in  a  rectangle  8  in.  long 
and  25%  as  wide? 

16.  A  rectangle  6  ft.  long  contains  18  sq.  ft.    What  is 
its  width  ?     Draw  the  figure. 

17.  What  is  the  perimeter  of  a  square  garden  contain- 
ing 25  square  rods? 

18.  A  man  bought  a  hat  for  $2.65.     What  4  pieces  of 
money  would  exactly  pay  for  it? 

19.  How  many  2-inch  squares  are  equal  to  a  6-inch 
square? 

20.  A  lady  having  $20  gave  50%  of  it  to  her  son  and 
50%  of  the  remainder  to  her  daughter.     How  much  had 
she  left?. 

21.  If  a  horse  trots  10  miles  in  an  hour,  how  far  does 
he  trot  in  6  minutes? 

22.  A  man  sold  a  cow  for  J  of  her  cost.     What  per 
cent  did  he  lose? 

23.  If  $50  is  f  of  my  cash,  how  much  have  I? 

24.  Helen's  age  is  25%  of  her  father's.     If  Helen's 
nge  is  8  years,  what  is  her  father's  age? 

25.  Mr.  Jones  pays  $300  a  year  for  rent,  which  is  10% 
of  the  value  of  the  house.     In  how  many  years  will  his 
rent  amount  to  the  value  of  the  house? 

Written  Work. 

378.     1.     Find  the  cost  of  25  bushels  of  wheat  at  $1.1 5 
a  bushel. 

2.  A  sheep  cost  $4,  a  cow  6  times  as  much,  and  a  horse 
3  times  as  much  as  the  cow.     They  all  cost  $ . 

3.  A  grocer  bought  a  barrel  of  vinegar  containing  42 
gallons  at  15#  a  gallon.     He  sold  it  at  6^  a  quart.     How 
much  did  he  gain? 


270  SCHOOL    ARITHMETIC. 

4.  The  distance  from  Pittsburg  to  Philadelphia  is  354 
miles.    At  2^  a  mile,  what  is  the  fare  for  a  round  trip? 

5.  How  long  is  the  side  of  a  square  whose  area  is  12J% 
of  that  of  a  rectangle  8  ft.  by  16  ft.? 

6.  A  lady  bought  8  yd.  of  silk  @  $1.25  a  yard,  3  pairs 
of  shoes  @  $2.50,  6  Ib.  of  butter  @  15#,  and  li  pk.  of 
apples  @  20^  a  half  peck.      Make  out  the  bill. 

7.  A  field  is  40  rods  long  and  16  rods  wide.    How  many 
square  rods  does  it  contain?    How  many  acres? 

8.  A  2-foot  cube  of  marble  was  polished  at  a  cost  of 
25^  a  square  foot.     How  much  was  paid  for  polishing? 

9.  How  many  square  yards  of  oilcloth  will  cover  a  room 
18  ft.  long  and  16  ft.  wide? 

10.  At  12J^  a  yard,  what  will  be  the  cost  of  36  yards 
of  cloth? 

11.  What  number  divided  by  12  will  give  the  quotient 
144? 

12.  How  many  boards,  each  12  ft.  long,  will  be  required 
for  a  fence  600  ft.  long,  and  5  boards  high? 

13.  From  a  cheese  which  weighed  75  Ib.  a  grocer  cut 
42  Ib.  8  oz.     How  much  remained? 

14.  There  are  16.5  ft.  in  a  rod.     How  many  feet  are 
there  in  320  rods,  or  1  mile? 

15.  How  many  rails,  each  30  ft.  long,  will  be  required 
for  a  mile  of  railroad? 

16.  A  fence  is  120  ft.  long  and  the  posts  are  8  ft.  apart. 
Find  how  many  posts  there  are.    Make  a  drawing. 

17.  If  2  bushels  of  oats  cost  64^,  what  is  the  cost  of  2 
pecks? 

18.  At  12i^  a  quart,  how  many  quarts  of  molasses  will 
$2  buy? 


GENERAL    REVIEW.  271 

19.  How  many  eggs,  at  10^  a  dozen,  can  be  bought  for 
$2.50? 

20.  Find   two   numbers   whose   product  is  105.     Two 
other  numbers. 

21.  In  an  orchard  -J  of  the  trees  are  apple,  3  peach, 
and  the  remainder  pear.     There  are  10  pear  trees.     How 
many  peach  trees? 

22.  On  Friday  a  man  started  on  a  trip.     He  was  gone 
24  days.     On.  what  day  of  the  week  did  he  return? 

23.  A  man  feeds  his  horse  6  qt.  of  oats  3  times  a  day. 
How  long  will  9  bushels  of  oats  last? 

24.  Does  your  pulse  beat  76  times  in  a  minute?    If  it 
does,  how  many  times  does  it  beat  in  a  day? 

25.  How  many  pint  bottles  will  it  take  to  hold   9i 
gal.  of  ink? 

26.  How  many  cubic  feet  of  water  can  be  put  into  a 
trough  6  ft.  long,  2  ft.  wide,  and  1  ft.  deep? 

27.  At  $2.40  a  square  yard,  what  will  it  cost  to  lay  a 
pavement  90  ft.  long  and  6  ft.  wide? 

28.  Find  the  interest  of  $50  for  4  mo.  at  6%. 

29.  I  lost  $5  by  selling  a  wagon  for  $35.     What  per 
cent  did  I  lose? 

30.  What  is  the  length  and  width  of  your  schoolroom  \ 
Find  the  cost  of  painting  the  ceiling  at  5^  a  square  yard. 


PRICE-LIST  OF  TEXT  BOOKS. 


1.  Johnson's  Primer  lin  colors),  Paper  Binding, 

2.  Johnson's  Primer  (in  colors),  Bound  in  Hoards 

3.  Johnson's  First  Header,  Hound  in   Hoards   

4.  Johnson's  First  Header,  Hound  in  Cloth 

5.  Johnson's  Second  Header.  Hound  in  Boards 

ti.     JobnsOn'a  Second  Reader.  Hound  in  Cloth  

7.  Johnson's  Third  Header,  Hound  in  Cloth 

8.  Johnson's  Fourth  Header,  Bound  in  Cloth 

9.  Johnson's  Fifth  Header,  Bound  in  Cloth  

10.  Branson's  Common  School  Speller,  First    Book  (In  Boards). 

11.  Branson's  Common  School  Speller,  Second  Book  (In  Boards)  .  

12.  Branson's  Common  School  Speller.  Complete  (In  Cloth) 

13.  Lee's  New  Primary    History   of  the   United  States   (formerly    Lee's 

Primary)  

3   hool  History  of  the  United  States,  Cloth 

Now  Scl 1  History  of  the  United  States.  Half  Morocco 

16.  Lee's  Advanced  School    History   of  the    United    States 

17.  Smithdeal's  Slant  Writing-Books,  (six  numbers),  each 

•J* *•*••« «in's  Vertical  Writing-Books  (Nos.  1,2,  3,  4),  each. 


Retail 
price. 


911274 


10 
15 
16 
20 
25 
30 
35 
45 
60 
ir, 
20 
30 

50 
75 
85 

100! 
05 
04 


Kxch'ge 

price. 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


52.  Southern  Literature  (from  1579  to  1895) 

53.  History  of  Vindnia  (Maurv's) 

54.  Geography  of  Virginia  (Henning's) 

55-  Moses'  First  Phonetic  Reader,  by  Prof.  E.  P.  Moses,  Raleigh,  N.  C. 
(Other  numbers  in  course  of  preparation) 

oli.  Some  Birds  and  Their  Ways,  cloth 

57.  Grimm's  Fairy  Tales,  by  P".  P.  Claxton  and  Winifred  Haliburton.  Cloth 


I  00 ' 
75 


35 


For  Examination,  with  compliments  of 

B.  F.  JOHNSON  PUBLISHING  CO.,  Publishers, 

RicHi-i-iorid,  Virginia. 


